Finite Group DatabasebetaFinite Group Databasebeta| order | 23264 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D727 |
| unambiguous semidirect product | C727⋊C25 |
| unambiguous semidirect product | (C2×C727)⋊C24 |
| Fitting, socle | C24×C727 ⋊ C2 |
| derived, Sylow | C727 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D727 |
| commutator, cosocle, hypocenter | C727 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C727 | C2 |
| LCS | G ▷ C727 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11632 |
5840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23264, 195);