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Elements of the group are displayed as words in the presentation $\langle a, b \mid b^{4632}=1, a^{96}=b^{2316}, b^{a}=b^{3337} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 193P | ||||||
| $C_{4632}.C_{96}$ | 1A | $1$ | $1$ | $C_{4632}.C_{96}$ | 1A | 1A | 1A | $1$ |
| $C_{4632}.C_{96}$ | 2A | $2$ | $1$ | $C_{4632}.C_{96}$ | 1A | 2A | 2A | $b^{2316}$ |
| $C_{4632}.C_{96}$ | 2B | $2$ | $193$ | $C_{12}\times C_{192}$ | 1A | 2B | 2B | $a^{48}b^{2262}$ |
| $C_{4632}.C_{96}$ | 2C | $2$ | $193$ | $C_{12}\times C_{192}$ | 1A | 2C | 2C | $a^{48}b^{2154}$ |
| $C_{4632}.C_{96}$ | 3A1 | $3$ | $1$ | $C_{4632}.C_{96}$ | 3A-1 | 1A | 3A1 | $b^{3088}$ |
| $C_{4632}.C_{96}$ | 3A-1 | $3$ | $1$ | $C_{4632}.C_{96}$ | 3A1 | 1A | 3A-1 | $b^{1544}$ |
| $C_{4632}.C_{96}$ | 3B1 | $3$ | $193$ | $C_{12}\times C_{192}$ | 3B-1 | 1A | 3B1 | $a^{32}b^{1276}$ |
| $C_{4632}.C_{96}$ | 3B-1 | $3$ | $193$ | $C_{12}\times C_{192}$ | 3B1 | 1A | 3B-1 | $a^{64}b^{2696}$ |
| $C_{4632}.C_{96}$ | 3C1 | $3$ | $193$ | $C_{12}\times C_{192}$ | 3C-1 | 1A | 3C1 | $a^{32}b^{2220}$ |
| $C_{4632}.C_{96}$ | 3C-1 | $3$ | $193$ | $C_{12}\times C_{192}$ | 3C1 | 1A | 3C-1 | $a^{64}b^{1104}$ |
| $C_{4632}.C_{96}$ | 3D1 | $3$ | $193$ | $C_{12}\times C_{192}$ | 3D-1 | 1A | 3D1 | $a^{32}b^{1748}$ |
| $C_{4632}.C_{96}$ | 3D-1 | $3$ | $193$ | $C_{12}\times C_{192}$ | 3D1 | 1A | 3D-1 | $a^{64}b^{4216}$ |
| $C_{4632}.C_{96}$ | 4A1 | $4$ | $1$ | $C_{4632}.C_{96}$ | 2A | 4A-1 | 4A1 | $b^{1158}$ |
| $C_{4632}.C_{96}$ | 4A-1 | $4$ | $1$ | $C_{4632}.C_{96}$ | 2A | 4A1 | 4A-1 | $b^{3474}$ |
| $C_{4632}.C_{96}$ | 4B1 | $4$ | $193$ | $C_{12}\times C_{192}$ | 2B | 4B-1 | 4B1 | $a^{24}b^{2739}$ |
| $C_{4632}.C_{96}$ | 4B-1 | $4$ | $193$ | $C_{12}\times C_{192}$ | 2B | 4B1 | 4B-1 | $a^{72}b^{681}$ |
| $C_{4632}.C_{96}$ | 4C1 | $4$ | $193$ | $C_{12}\times C_{192}$ | 2B | 4C-1 | 4C1 | $a^{24}b^{4431}$ |
| $C_{4632}.C_{96}$ | 4C-1 | $4$ | $193$ | $C_{12}\times C_{192}$ | 2B | 4C1 | 4C-1 | $a^{72}b^{3405}$ |
| $C_{4632}.C_{96}$ | 4D1 | $4$ | $193$ | $C_{12}\times C_{192}$ | 2C | 4D-1 | 4D1 | $a^{24}b^{3585}$ |
| $C_{4632}.C_{96}$ | 4D-1 | $4$ | $193$ | $C_{12}\times C_{192}$ | 2C | 4D1 | 4D-1 | $a^{72}b^{2043}$ |
| $C_{4632}.C_{96}$ | 4E1 | $4$ | $193$ | $C_{12}\times C_{192}$ | 2C | 4E-1 | 4E1 | $a^{24}b^{645}$ |
| $C_{4632}.C_{96}$ | 4E-1 | $4$ | $193$ | $C_{12}\times C_{192}$ | 2C | 4E1 | 4E-1 | $a^{72}b^{135}$ |
| $C_{4632}.C_{96}$ | 4F1 | $4$ | $193$ | $C_{12}\times C_{192}$ | 2A | 4F-1 | 4F1 | $a^{48}b^{4068}$ |
| $C_{4632}.C_{96}$ | 4F-1 | $4$ | $193$ | $C_{12}\times C_{192}$ | 2A | 4F1 | 4F-1 | $a^{48}b^{1752}$ |
| $C_{4632}.C_{96}$ | 6A1 | $6$ | $1$ | $C_{4632}.C_{96}$ | 3A-1 | 2A | 6A1 | $b^{772}$ |
| $C_{4632}.C_{96}$ | 6A-1 | $6$ | $1$ | $C_{4632}.C_{96}$ | 3A1 | 2A | 6A-1 | $b^{3860}$ |
| $C_{4632}.C_{96}$ | 6B1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3B1 | 2B | 6B1 | $a^{16}b^{338}$ |
| $C_{4632}.C_{96}$ | 6B-1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3B-1 | 2B | 6B-1 | $a^{80}b^{2530}$ |
| $C_{4632}.C_{96}$ | 6C1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3C1 | 2B | 6C1 | $a^{16}b^{3042}$ |
| $C_{4632}.C_{96}$ | 6C-1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3C-1 | 2B | 6C-1 | $a^{80}b^{4242}$ |
| $C_{4632}.C_{96}$ | 6D1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3D1 | 2B | 6D1 | $a^{16}b^{1690}$ |
| $C_{4632}.C_{96}$ | 6D-1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3D-1 | 2B | 6D-1 | $a^{80}b^{3386}$ |
| $C_{4632}.C_{96}$ | 6E1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3C1 | 2C | 6E1 | $a^{16}b^{1014}$ |
| $C_{4632}.C_{96}$ | 6E-1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3C-1 | 2C | 6E-1 | $a^{80}b^{2958}$ |
| $C_{4632}.C_{96}$ | 6F1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3A1 | 2C | 6F1 | $a^{48}b^{3170}$ |
| $C_{4632}.C_{96}$ | 6F-1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3A-1 | 2C | 6F-1 | $a^{48}b^{82}$ |
| $C_{4632}.C_{96}$ | 6G1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3A1 | 2B | 6G1 | $a^{48}b^{4166}$ |
| $C_{4632}.C_{96}$ | 6G-1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3A-1 | 2B | 6G-1 | $a^{48}b^{1078}$ |
| $C_{4632}.C_{96}$ | 6H1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3D1 | 2C | 6H1 | $a^{16}b^{3718}$ |
| $C_{4632}.C_{96}$ | 6H-1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3D-1 | 2C | 6H-1 | $a^{80}b^{38}$ |
| $C_{4632}.C_{96}$ | 6I1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3B1 | 2C | 6I1 | $a^{16}b^{2366}$ |
| $C_{4632}.C_{96}$ | 6I-1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3B-1 | 2C | 6I-1 | $a^{80}b^{3814}$ |
| $C_{4632}.C_{96}$ | 6J1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3B-1 | 2A | 6J1 | $a^{32}b^{2896}$ |
| $C_{4632}.C_{96}$ | 6J-1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3B1 | 2A | 6J-1 | $a^{64}b^{1436}$ |
| $C_{4632}.C_{96}$ | 6K1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3D1 | 2A | 6K1 | $a^{64}b^{748}$ |
| $C_{4632}.C_{96}$ | 6K-1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3D-1 | 2A | 6K-1 | $a^{32}b^{3560}$ |
| $C_{4632}.C_{96}$ | 6L1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3C-1 | 2A | 6L1 | $a^{32}b^{2904}$ |
| $C_{4632}.C_{96}$ | 6L-1 | $6$ | $193$ | $C_{12}\times C_{192}$ | 3C1 | 2A | 6L-1 | $a^{64}b^{3660}$ |
| $C_{4632}.C_{96}$ | 8A1 | $8$ | $1$ | $C_{4632}.C_{96}$ | 4A1 | 8A3 | 8A1 | $b^{2895}$ |
| $C_{4632}.C_{96}$ | 8A-1 | $8$ | $1$ | $C_{4632}.C_{96}$ | 4A-1 | 8A-3 | 8A-1 | $b^{1737}$ |