Finite Group DatabasebetaFinite Group Databasebeta| order | 2496 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C2×#11929141 |
| Fitting | C2×C13×#41 ⋊ C2×C3 |
| Hall | C2×#88256 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×H(5,𝔽2) |
| Sylow | C13 ⋊ C2×C3×H(5,𝔽2) |
1796 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 5 generators on 23 points:
(1,2)(11,12,18)(13,20,23)(14,16,19)(15,22,17);(4,8)(7,10)(12,13)(14,16)(15,19)(17,18)(20,21)(22,23);(3,5,6,9)(4,7,8,10);(3,4,6,8)(5,7,9,10);(5,9)(7,10)142 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2)(11,12,18)(13,20,23)(14,16,19)(15,22,17), (4,8)(7,10)(12,13)(14,16)(15,19)(17,18)(20,21)(22,23), (3,5,6,9)(4,7,8,10), (3,4,6,8)(5,7,9,10), (5,9)(7,10));