Finite Group DatabasebetaFinite Group Databasebeta| order | 24534 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D1363 |
| unambiguous semidirect product | C29⋊(C32×D47) |
| unambiguous semidirect product | C47⋊(C32×D29) |
| Fitting, socle, Hall | C32×C29×C47 ⋊ C2 |
| derived, Hall | C29×C47 ⋊ C2×C32 |
| Hall | C32×C47 ⋊ D29 |
| Hall | C32×C29 ⋊ D47 |
| Sylow | C47 ⋊ C32×D29 |
| Sylow | C29 ⋊ C32×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D1363 |
| commutator, cosocle, hypocenter | C29×C47 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29×C47 | C2 |
| LCS | G ▷ C29×C47 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12267 |
6147 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24534, 12);