Finite Group DatabasebetaFinite Group Databasebeta| order | 23529 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11×C23 · Schur multiplier (H2) = C1 |
| direct product | C11×C23×C31⋊C3 |
| unambiguous semidirect product | C31⋊(C3×C11×C23) |
| unambiguous semidirect product | (C11×C31)⋊(C3×C23) |
| unambiguous semidirect product | (C11×C23×C31)⋊C3 |
| Fitting, socle, Hall | C11×C23×C31 ⋊ C3 |
| derived, Sylow | C31 ⋊ C3×C11×C23 |
| Hall | C23×C31 ⋊ C3×C11 |
| Hall | C11×C31 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C23 | C31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C3×C11×C23 |
| Frattini | C1 | G |
| Fitting, socle | C11×C23×C31 | C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C11×C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7843 |
3289 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23529, 3);