Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#11796888 |
| Sylow | C32 ⋊ C22×#361 |
3768 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)(5,13)(6,15)(7,14)(10,17)(11,16)(12,18);(3,4,5,9,14,17,6,16,8,12,15,18,7,11,13,10)(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)(5,13)(6,15)(7,14)(10,17)(11,16)(12,18), (3,4,5,9,14,17,6,16,8,12,15,18,7,11,13,10)(23,24));