diff --git a/CMakeLists.txt b/CMakeLists.txt
index 4b615b6..e6b2952 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -11,7 +11,9 @@ include(External/eigen.cmake)
 include(External/glad.cmake)
 include(External/json.cmake)
 
-include_directories(./include)
+include_directories(include)
+
+add_subdirectory(tc)
 
 add_custom_target(resources DEPENDS resources_output)
 add_custom_command(
@@ -31,3 +33,6 @@ add_dependencies(vis resources)
 
 add_executable(serial src/serialtest.cpp)
 target_link_libraries(serial eigen nlohmann_json)
+
+add_executable(tctest src/tctest.cpp)
+target_link_libraries(tctest PUBLIC eigen tc)
diff --git a/src/tctest.cpp b/src/tctest.cpp
new file mode 100644
index 0000000..50360ac
--- /dev/null
+++ b/src/tctest.cpp
@@ -0,0 +1,11 @@
+#include <tc/core.hpp>
+#include <tc/groups.hpp>
+#include <Eigen/Eigen>
+#include <iostream>
+
+int main() {
+    auto group = tc::group::H(4);
+    auto cos = group.solve({});
+
+    std::cout << cos.size() << std::endl;
+}
diff --git a/tc/CMakeLists.txt b/tc/CMakeLists.txt
new file mode 100644
index 0000000..2ffa85a
--- /dev/null
+++ b/tc/CMakeLists.txt
@@ -0,0 +1,8 @@
+add_library(tc
+    include/tc/groups.hpp
+    src/groups.cpp
+    include/tc/core.hpp
+    src/core.cpp
+    src/solve.cpp)
+
+target_include_directories(tc PUBLIC include)
diff --git a/tc/include/tc/core.hpp b/tc/include/tc/core.hpp
new file mode 100644
index 0000000..81cb556
--- /dev/null
+++ b/tc/include/tc/core.hpp
@@ -0,0 +1,165 @@
+#pragma once
+
+#include <array>
+#include <functional>
+#include <vector>
+#include <string>
+
+namespace tc {
+    struct Action {
+        int from_idx = -1;
+        int gen = -1;
+
+        Action() = default;
+
+        Action(const Action &) = default;
+
+        Action(int from_idx, int gen);
+    };
+
+    struct Path {
+        std::vector<Action> path;
+
+        Path() = default;
+
+        Path(const Path &) = default;
+
+        void add_row();
+
+        [[nodiscard]] Action get(int to_idx) const;
+
+        void put(int from_idx, int gen, int to_idx);
+
+        template<class C, class T, class E>
+        void walk(
+            C& res,
+            T start,
+            std::vector<E> gens,
+            std::function<T(const T &, const E &)> op
+        ) const {
+            size_t s = size();
+            res.reserve(s);
+            res.push_back(start);
+
+            for (int i = 1; i < s; ++i) {
+                auto &action = path[i];
+                auto &from = res.get(action.from_idx);
+                auto &val = gens[action.gen];
+                res.push_back(op(from,val));
+            }
+        }
+
+        template<class T, class E>
+        [[nodiscard]] std::vector<T> walk(
+            T start,
+            std::vector<E> gens,
+            std::function<T(const T &, const E &)> op
+        ) const {
+            std::vector<T> res;
+            res.reserve(size());
+            res.push_back(start);
+
+            for (int i = 1; i < size(); ++i) {
+                auto &action = path[i];
+                auto &from = res[action.from_idx];
+                auto &val = gens[action.gen];
+                res.push_back(op(from, val));
+            }
+
+            return res;
+        }
+
+        template<class T>
+        [[nodiscard]] std::vector<T> walk(
+            T start,
+            std::function<T(const T &, const int &)> op
+        ) const {
+            std::vector<T> res;
+            res.reserve(size());
+            res.push_back(start);
+
+            for (int i = 1; i < size(); ++i) {
+                auto &action = path[i];
+                auto &from = res[action.from_idx];
+                auto &val = action.gen;
+                res[i] = op(from, val);
+            }
+
+            return res;
+        }
+
+        [[nodiscard]] size_t size() const;
+    };
+
+    struct Cosets {
+        int ngens;
+        std::vector<int> data;
+        Path path;
+
+        Cosets(const Cosets &) = default;
+
+        explicit Cosets(int ngens);
+
+        void add_row();
+
+        void put(int coset, int gen, int target);
+
+        void put(int idx, int target);
+
+        [[nodiscard]] int get(int coset, int gen) const;
+
+        [[nodiscard]] int get(int idx) const;
+
+        [[nodiscard]] size_t size() const;
+    };
+
+    struct Rel {
+        std::array<int, 2> gens;
+        int mult;
+
+        Rel() = default;
+
+        Rel(const Rel &) = default;
+
+        Rel(int a, int b, int m);
+
+        [[nodiscard]] Rel shift(int off) const;
+    };
+
+    struct SubGroup;
+
+    struct Group {
+        int ngens;
+        std::vector<std::vector<int>> _mults;
+        std::string name;
+
+        Group(const Group &) = default;
+
+        explicit Group(int ngens, const std::vector<Rel> &rels = {}, std::string name = "G");
+
+        void set(const Rel &r);
+
+        [[nodiscard]] int get(int a, int b) const;
+
+        [[nodiscard]] std::vector<Rel> rels() const;
+
+        [[nodiscard]] SubGroup subgroup(const std::vector<int> &gens) const;
+
+        [[nodiscard]] Group product(const Group &other) const;
+
+        [[nodiscard]] Group power(int p) const;
+
+        [[nodiscard]] Cosets solve(const std::vector<int> &sub_gens = {}) const;
+    };
+
+    struct SubGroup : public Group {
+        std::vector<int> gen_map;
+        const Group &parent;
+
+        SubGroup(const Group &parent, std::vector<int> gen_map);
+    };
+
+    Group operator*(const Group &g, const Group &h);
+
+    Group operator^(const Group &g, int p);
+}
diff --git a/tc/include/tc/groups.hpp b/tc/include/tc/groups.hpp
new file mode 100644
index 0000000..7a3e421
--- /dev/null
+++ b/tc/include/tc/groups.hpp
@@ -0,0 +1,70 @@
+#pragma once
+
+#include "core.hpp"
+
+
+namespace tc {
+    /**
+     * Construct a group from a (simplified) Schlafli Symbol of the form [a, b, ..., c]
+     * @param mults: The sequence of multiplicites between adjacent generators.
+     */
+    Group schlafli(const std::vector<int> &mults, const std::string &name);
+
+    /**
+     * Construct a group from a (simplified) Schlafli Symbol of the form [a, b, ..., c]
+     * @param mults: The sequence of multiplicites between adjacent generators.
+     */
+    Group schlafli(const std::vector<int> &mults);
+
+    namespace group {
+        /**
+         * Simplex
+         */
+        Group A(int dim);
+
+        /**
+         * Cube, Orthoplex
+         */
+        Group B(int dim);
+
+        /**
+         * Demicube, Orthoplex
+         */
+        Group D(int dim);
+
+        /**
+         * E groups
+         */
+        Group E(int dim);
+
+        /**
+         * 24 Cell
+         */
+        Group F4();
+
+        /**
+         * Hexagon
+         */
+        Group G2();
+
+        /**
+         * Icosahedron
+         */
+        Group H(int dim);
+
+        /**
+         * Polygonal
+         */
+        Group I2(int n);
+
+        /**
+         * Toroidal. I2(n) * I2(m)
+         */
+        Group T(int n, int m);
+
+        /**
+         * Toroidal. T(n, n)
+         */
+        Group T(int n);
+    }
+}
diff --git a/tc/src/core.cpp b/tc/src/core.cpp
new file mode 100644
index 0000000..09ff19d
--- /dev/null
+++ b/tc/src/core.cpp
@@ -0,0 +1,161 @@
+#include "tc/core.hpp"
+
+#include <utility>
+#include <sstream>
+#include <algorithm>
+
+namespace tc {
+    Action::Action(int from_idx, int gen)
+        : from_idx(from_idx), gen(gen) {
+    }
+
+    void Path::add_row() {
+        path.resize(path.size() + 1);
+    }
+
+    Action Path::get(int to_idx) const {
+        return path[to_idx];
+    }
+
+    void Path::put(int from_idx, int gen, int to_idx) {
+        path[to_idx] = Action(from_idx, gen);
+    }
+
+    size_t Path::size() const {
+        return path.size();
+    }
+
+    Cosets::Cosets(int ngens)
+        : ngens(ngens) {
+    }
+
+    void Cosets::add_row() {
+        data.resize(data.size() + ngens, -1);
+        path.add_row();
+    }
+
+    void Cosets::put(int coset, int gen, int target) {
+        data[coset * ngens + gen] = target;
+        data[target * ngens + gen] = coset;
+
+        if (path.get(target).from_idx == -1) {
+            path.put(coset, gen, target);
+        }
+    }
+
+    void Cosets::put(int idx, int target) {
+        int coset = idx / ngens;
+        int gen = idx % ngens;
+        data[idx] = target;
+        data[target * ngens + gen] = coset;
+
+        if (path.get(target).from_idx == -1) {
+            path.put(coset, gen, target);
+        }
+    }
+
+    int Cosets::get(int coset, int gen) const {
+        return data[coset * ngens + gen];
+    }
+
+    int Cosets::get(int idx) const {
+        return data[idx];
+    }
+
+    size_t Cosets::size() const {
+        return path.size();
+    }
+
+    Rel::Rel(int a, int b, int m)
+        : gens({a, b}), mult(m) {
+    }
+
+    Rel Rel::shift(int off) const {
+        return Rel(gens[0] + off, gens[1] + off, mult);
+    }
+
+    Group::Group(int ngens, const std::vector<Rel> &rels, std::string name)
+        : ngens(ngens), name(std::move(name)) {
+        _mults.resize(ngens);
+
+        for (auto &mult : _mults) {
+            mult.resize(ngens, 2);
+        }
+
+        for (const auto &rel : rels) {
+            set(rel);
+        }
+    }
+
+    void Group::set(const Rel &r) {
+        _mults[r.gens[0]][r.gens[1]] = r.mult;
+        _mults[r.gens[1]][r.gens[0]] = r.mult;
+    }
+
+    int Group::get(int a, int b) const {
+        return _mults[a][b];
+    }
+
+    std::vector<Rel> Group::rels() const {
+        std::vector<Rel> res;
+        for (int i = 0; i < ngens - 1; ++i) {
+            for (int j = i + 1; j < ngens; ++j) {
+                res.emplace_back(i, j, get(i, j));
+            }
+        }
+        return res;
+    }
+
+    SubGroup Group::subgroup(const std::vector<int> &gens) const {
+        return SubGroup(*this, gens);
+    }
+
+    Group Group::product(const Group &other) const {
+        std::stringstream ss;
+        ss << name << "*" << other.name;
+
+        Group g(ngens + other.ngens, rels(), ss.str());
+
+        for (const auto &rel : other.rels()) {
+            g.set(rel.shift(ngens));
+        }
+
+        return g;
+    }
+
+    Group Group::power(int p) const {
+        std::stringstream ss;
+        ss << name << "^" << p;
+
+        Group g(ngens * p, {}, ss.str());
+        for (const auto &rel : rels()) {
+            for (int off = 0; off < g.ngens; off += ngens) {
+                g.set(rel.shift(off));
+            }
+        }
+
+        return g;
+    }
+
+    SubGroup::SubGroup(const Group &parent, std::vector<int> gen_map)
+        : Group(gen_map.size()), parent(parent) {
+
+        std::sort(gen_map.begin(), gen_map.end());
+        this->gen_map = gen_map;
+
+        for (size_t i = 0; i < gen_map.size(); ++i) {
+            for (size_t j = 0; j < gen_map.size(); ++j) {
+                int mult = parent.get(gen_map[i], gen_map[j]);
+                set(Rel(i, j, mult));
+            }
+        }
+    }
+
+    Group operator*(const Group &g, const Group &h) {
+        return g.product(h);
+    }
+
+    Group operator^(const Group &g, int p) {
+        return g.power(p);
+    }
+}
diff --git a/tc/src/groups.cpp b/tc/src/groups.cpp
new file mode 100644
index 0000000..1cebc12
--- /dev/null
+++ b/tc/src/groups.cpp
@@ -0,0 +1,120 @@
+#include "tc/groups.hpp"
+
+#include <sstream>
+
+namespace tc {
+    Group schlafli(const std::vector<int> &mults, const std::string &name) {
+        int ngens = (int) mults.size() + 1;
+
+        Group g(ngens, {}, name);
+
+        for (int i = 0; i < (int) mults.size(); i++) {
+            g.set(Rel(i, i + 1, mults[i]));
+        }
+
+        return g;
+    }
+
+    Group schlafli(const std::vector<int> &mults) {
+        std::stringstream ss;
+        ss << "[";
+        if (!mults.empty()) {
+            for (size_t i = 0; i < mults.size() - 1; ++i) {
+                ss << mults[i] << ",";
+            }
+            ss << mults.back();
+        }
+        ss << "]";
+
+        return schlafli(mults, ss.str());
+    }
+
+    namespace group {
+        Group A(const int dim) {
+            std::stringstream ss;
+            ss << "A(" << dim << ")";
+
+            if (dim == 0)
+                return Group(0, {}, ss.str());
+
+            const std::vector<int> &mults = std::vector<int>(dim - 1, 3);
+
+            return schlafli(mults, ss.str());
+        }
+
+        Group B(const int dim) {
+            std::stringstream ss;
+            ss << "B(" << dim << ")";
+
+            std::vector<int> mults(dim - 1, 3);
+            mults[0] = 4;
+
+            return schlafli(mults, ss.str());
+        }
+
+        Group D(const int dim) {
+            std::stringstream ss;
+            ss << "D(" << dim << ")";
+
+            std::vector<int> mults(dim - 1, 3);
+            mults[dim - 2] = 2;
+
+            Group g = schlafli(mults, ss.str());
+            g.set(Rel(1, dim - 1, 3));
+
+            return g;
+        }
+
+        Group E(const int dim) {
+            std::stringstream ss;
+            ss << "E(" << dim << ")";
+
+            std::vector<int> mults(dim - 1, 3);
+            mults[dim - 2] = 2;
+
+            Group g = schlafli(mults, ss.str());
+            g.set(Rel(2, dim - 1, 3));
+
+            return g;
+        }
+
+        Group F4() {
+            return schlafli({3, 4, 3}, "F4");
+        }
+
+        Group G2() {
+            return schlafli({6}, "G2");
+        }
+
+        Group H(const int dim) {
+            std::stringstream ss;
+            ss << "H(" << dim << ")";
+
+            std::vector<int> mults(dim - 1, 3);
+            mults[0] = 5;
+
+            return schlafli(mults, ss.str());
+        }
+
+        Group I2(const int n) {
+            std::stringstream ss;
+            ss << "I2(" << n << ")";
+
+            return schlafli({n}, ss.str());
+        }
+
+        Group T(const int n, const int m) {
+            std::stringstream ss;
+            ss << "T(" << n << "," << m << ")";
+
+            return schlafli({n, 2, m}, ss.str());
+        }
+
+        Group T(const int n) {
+            std::stringstream ss;
+            ss << "T(" << n << ")";
+
+            return schlafli({n, 2, n}, ss.str());
+        }
+    }
+}
diff --git a/tc/src/solve.cpp b/tc/src/solve.cpp
new file mode 100644
index 0000000..0c144f0
--- /dev/null
+++ b/tc/src/solve.cpp
@@ -0,0 +1,189 @@
+#include "tc/core.hpp"
+
+#include <algorithm>
+
+namespace tc {
+    struct RelTablesRow {
+        int *gnrs;
+        int **lst_ptrs;
+
+        RelTablesRow(int N, int *gnrs, int **lst_ptrs) : gnrs(gnrs), lst_ptrs(lst_ptrs) {
+            for (int i = 0; i < N; i++) {
+                lst_ptrs[i] = nullptr;
+            }
+        }
+    };
+
+    struct RelTables {
+        static const int ROW_BLOCK_SIZE = 64;
+        std::vector<Rel> rels;
+        std::vector<RelTablesRow *> rows;
+        int start = 0;
+        int num_tables;
+        int buffer_rows = 0;
+
+        explicit RelTables(const std::vector<Rel> &rels)
+            : num_tables(rels.size()), rels(rels) {
+        }
+
+        void add_row() {
+            if (buffer_rows == 0) {
+                int *gnrs_alloc = new int[num_tables * RelTables::ROW_BLOCK_SIZE];
+                int **lst_ptrs_alloc = new int *[num_tables * RelTables::ROW_BLOCK_SIZE];
+                for (int i = 0; i < RelTables::ROW_BLOCK_SIZE; i++) {
+                    rows.push_back(
+                        new RelTablesRow(num_tables, &gnrs_alloc[i * num_tables], &lst_ptrs_alloc[i * num_tables]));
+                }
+                buffer_rows = RelTables::ROW_BLOCK_SIZE;
+            }
+
+            buffer_rows--;
+        }
+
+        void del_rows_to(int idx) {
+            const int del_to = (idx / RelTables::ROW_BLOCK_SIZE) * RelTables::ROW_BLOCK_SIZE;
+            for (int i = start; i < del_to; i += RelTables::ROW_BLOCK_SIZE) {
+                delete[] rows[i]->gnrs;
+                delete[] rows[i]->lst_ptrs;
+                for (int j = 0; j < RelTables::ROW_BLOCK_SIZE; j++) {
+                    delete rows[i + j];
+                }
+                start += RelTables::ROW_BLOCK_SIZE;
+            }
+        }
+
+        ~RelTables() {
+            while (start < rows.size()) {
+                delete[] rows[start]->gnrs;
+                delete[] rows[start]->lst_ptrs;
+                for (int j = 0; j < RelTables::ROW_BLOCK_SIZE; j++) {
+                    delete rows[start + j];
+                }
+                start += RelTables::ROW_BLOCK_SIZE;
+            }
+        }
+    };
+
+    Cosets Group::solve(const std::vector<int> &sub_gens) const {
+        Cosets cosets(ngens);
+        cosets.add_row();
+
+        if (ngens == 0) {
+            return cosets;
+        }
+
+        for (int g : sub_gens) {
+            if (g < ngens)
+                cosets.put(0, g, 0);
+        }
+
+        RelTables rel_tables(rels());
+        std::vector<std::vector<int>> gen_map(ngens);
+        int rel_idx = 0;
+        for (Rel m : rels()) {
+            gen_map[m.gens[0]].push_back(rel_idx);
+            gen_map[m.gens[1]].push_back(rel_idx);
+            rel_idx++;
+        }
+
+        int null_lst_ptr;
+        rel_tables.add_row();
+        RelTablesRow &row = *(rel_tables.rows[0]);
+        for (int table_idx = 0; table_idx < rel_tables.num_tables; table_idx++) {
+            Rel &ti = rel_tables.rels[table_idx];
+
+            if (cosets.get(ti.gens[0]) + cosets.get(ti.gens[1]) == -2) {
+                row.lst_ptrs[table_idx] = new int;
+                row.gnrs[table_idx] = 0;
+            } else {
+                row.lst_ptrs[table_idx] = &null_lst_ptr;
+                row.gnrs[table_idx] = -1;
+            }
+        }
+
+        int idx = 0;
+        int coset, gen, target, fact_idx, lst, gen_;
+        while (true) {
+            while (idx < cosets.data.size() and cosets.get(idx) >= 0)
+                idx++;
+
+            if (idx == cosets.data.size()) {
+                rel_tables.del_rows_to(idx / ngens);
+                break;
+            }
+
+            target = cosets.size();
+            cosets.add_row();
+            rel_tables.add_row();
+
+            std::vector<int> facts;
+            facts.push_back(idx);
+
+            coset = idx / ngens;
+            gen = idx % ngens;
+
+            rel_tables.del_rows_to(coset);
+
+            RelTablesRow &target_row = *(rel_tables.rows[target]);
+            while (!facts.empty()) {
+                fact_idx = facts.back();
+                facts.pop_back();
+
+                if (cosets.get(fact_idx) != -1)
+                    continue;
+
+                cosets.put(fact_idx, target);
+
+                coset = fact_idx / ngens;
+                gen = fact_idx % ngens;
+
+                if (target == coset)
+                    for (int table_idx : gen_map[gen])
+                        if (target_row.lst_ptrs[table_idx] == nullptr)
+                            target_row.gnrs[table_idx] = -1;
+
+                RelTablesRow &coset_row = *(rel_tables.rows[coset]);
+                for (int table_idx : gen_map[gen]) {
+                    if (target_row.lst_ptrs[table_idx] == nullptr) {
+                        Rel &ti = rel_tables.rels[table_idx];
+                        target_row.lst_ptrs[table_idx] = coset_row.lst_ptrs[table_idx];
+                        target_row.gnrs[table_idx] = coset_row.gnrs[table_idx] + 1;
+
+                        if (coset_row.gnrs[table_idx] < 0)
+                            target_row.gnrs[table_idx] -= 2;
+
+                        if (target_row.gnrs[table_idx] == ti.mult) {
+                            lst = *(target_row.lst_ptrs[table_idx]);
+                            delete target_row.lst_ptrs[table_idx];
+                            gen_ = ti.gens[(int) (ti.gens[0] == gen)];
+                            facts.push_back(lst * ngens + gen_);
+                        } else if (target_row.gnrs[table_idx] == -ti.mult) {
+                            gen_ = ti.gens[ti.gens[0] == gen];
+                            facts.push_back(target * ngens + gen_);
+                        } else if (target_row.gnrs[table_idx] == ti.mult - 1) {
+                            *(target_row.lst_ptrs[table_idx]) = target;
+                        }
+                    }
+                }
+
+                std::sort(facts.begin(), facts.end(), std::greater<>());
+            }
+
+            for (int table_idx = 0; table_idx < rel_tables.num_tables; table_idx++) {
+                Rel &ti = rel_tables.rels[table_idx];
+                if (target_row.lst_ptrs[table_idx] == nullptr) {
+                    if ((cosets.get(target, ti.gens[0]) != target) and
+                        (cosets.get(target, ti.gens[1]) != target)) {
+                        target_row.lst_ptrs[table_idx] = new int;
+                        target_row.gnrs[table_idx] = 0;
+                    } else {
+                        target_row.lst_ptrs[table_idx] = &null_lst_ptr;
+                        target_row.gnrs[table_idx] = -1;
+                    }
+                }
+            }
+        }
+
+        return cosets;
+    }
+}