Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#11796827 |
| Fitting | C2×C32×#106 ⋊ C22 |
| Sylow | C32 ⋊ C22×#360 |
2728 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 24 points:
(20,21)(22,23);(1,2)(19,20,21);(4,9,12,17)(5,13)(6,16)(7,14)(10,11,15,18);(3,4,5,10,7,11,13,17,8,12,6,15,14,18,16,9)(23,24)156 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((20,21)(22,23), (1,2)(19,20,21), (4,9,12,17)(5,13)(6,16)(7,14)(10,11,15,18), (3,4,5,10,7,11,13,17,8,12,6,15,14,18,16,9)(23,24));