Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24 |
| direct product | D3×#7182 |
| Fitting | C3×#7182 ⋊ C2 |
| Sylow | C3 ⋊ C2×#7182 |
1212 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,3);(1,2,3)(9,14,15,16,18,19,17,23)(10,11)(21,22);(4,5,6,7)(8,9,11,14,20,17,21,23,13,18,10,19,12,15,22,16)192 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((2,3), (1,2,3)(9,14,15,16,18,19,17,23)(10,11)(21,22), (4,5,6,7)(8,9,11,14,20,17,21,23,13,18,10,19,12,15,22,16));