Finite Group DatabasebetaFinite Group Databasebeta| order | 23364 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×Dic649 |
| unambiguous semidirect product | C11⋊(C9×Dic59) |
| unambiguous semidirect product | C59⋊(C9×Dic11) |
| derived, Hall | C11×C59 ⋊ C4×C9 |
| Hall | C9×C11×C59 ⋊ C4 |
| Hall | C9×C59 ⋊ Dic11 |
| Hall | C9×C11 ⋊ Dic59 |
| Sylow | C59 ⋊ C9×Dic11 |
| Sylow | C11 ⋊ C9×Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D649 |
| commutator, hypocenter | C11×C59 | C4×C9 |
| Frattini | C2×C3 | C3×D649 |
| Fitting | C2×C9×C11×C59 | C2 |
| socle, prime radical, cosocle | C2×C3×C11×C59 | C2×C3 |
| LCS | G ▷ C11×C59 | |
| UCS | C1 ◁ C2×C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23364 |
5868 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23364, 4);