Finite Group DatabasebetaFinite Group Databasebeta| order | 32131 |
| automorphism | ? |
| homology | Abelianization (H1) = C11×C127 · Schur multiplier (H2) = C1 |
| direct product | C127×C23⋊C11 |
| unambiguous semidirect product | C23⋊(C11×C127) |
| unambiguous semidirect product | (C23×C127)⋊C11 |
| Fitting, socle, Hall | C23×C127 ⋊ C11 |
| derived, Sylow | C23 ⋊ C11×C127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C127 | C23⋊C11 |
| commutator, cosocle, hypocenter | C23 | C11×C127 |
| Frattini | C1 | G |
| Fitting, socle | C23×C127 | C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C127 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2921 |
1651 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32131, 1);