Finite Group DatabasebetaFinite Group Databasebeta| order | 24564 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C89 · Schur multiplier (H2) = C1 |
| direct product | C89×Dic69 |
| unambiguous semidirect product | C3⋊(C89×Dic23) |
| unambiguous semidirect product | C23⋊(Dic3×C89) |
| derived, Hall | C3×C23 ⋊ C4×C89 |
| Hall | C3×C23×C89 ⋊ C4 |
| Hall | C23×C89 ⋊ Dic3 |
| Hall | C3×C89 ⋊ Dic23 |
| Sylow | C23 ⋊ Dic3×C89 |
| Sylow | C3 ⋊ C89×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C89 | D69 |
| commutator, hypocenter | C3×C23 | C4×C89 |
| Frattini | C2 | C89×D69 |
| Fitting, socle, prime radical | C2×C3×C23×C89 | C2 |
| cosocle | C2×C3×C23 | C2×C89 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C2×C89 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24564 |
6408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24564, 7);