Finite Group DatabasebetaFinite Group Databasebeta| order | 24564 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic2047 |
| unambiguous semidirect product | C23⋊(C3×Dic89) |
| derived, Hall | C23×C89 ⋊ C3×C4 |
| Hall | C3×C23×C89 ⋊ C4 |
| Hall | C3×C89 ⋊ Dic23 |
| Sylow | C89 ⋊ C3×Dic23 |
| Hall | C3×C23 ⋊ Dic89 |
| Sylow | C23 ⋊ C3×Dic89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D2047 |
| commutator, hypocenter | C23×C89 | C3×C4 |
| Frattini | C2 | C3×D2047 |
| Fitting, socle, prime radical | C2×C3×C23×C89 | C2 |
| cosocle | C2×C23×C89 | C2×C3 |
| LCS | G ▷ C23×C89 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24564 |
6150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24564, 4);