Finite Group DatabasebetaFinite Group Databasebeta| order | 24012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×C23×D29 |
| unambiguous semidirect product | C29⋊(C22×C9×C23) |
| unambiguous semidirect product | (C2×C29)⋊(C2×C9×C23) |
| Fitting | C2×C9×C23×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C22×C9×C23 |
| Hall | C9×C23×C29 ⋊ C22 |
| Hall | C23×C29 ⋊ C22×C9 |
| Hall | C9×C29 ⋊ C22×C23 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12006 |
6624 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24012, 28);