Finite Group DatabasebetaFinite Group Databasebeta| order | 23114 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1651 |
| unambiguous semidirect product | C13⋊(C7×D127) |
| Fitting, socle, Hall | C7×C13×C127 ⋊ C2 |
| derived, Hall | C13×C127 ⋊ C2×C7 |
| Hall | C7×C127 ⋊ D13 |
| Sylow | C127 ⋊ C7×D13 |
| Hall | C7×C13 ⋊ D127 |
| Sylow | C13 ⋊ C7×D127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1651 |
| commutator, cosocle, hypocenter | C13×C127 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C127 | C2 |
| LCS | G ▷ C13×C127 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11557 |
5789 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23114, 5);