Finite Group DatabasebetaFinite Group Databasebeta| order | 23114 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C13⋊(D127⋊C7) |
| unambiguous semidirect product | (C127⋊C7)⋊D13 |
| unambiguous semidirect product | D1651⋊C7 |
| Fitting, socle, derived, Hall | C13×C127 ⋊ C2×C7 |
| Hall | C13×C127⋊C7 ⋊ C2 |
| Hall | D1651 ⋊ C7 |
| Hall | C127⋊C7 ⋊ D13 |
| Sylow | C127 ⋊ C7×D13 |
| Sylow | C13 ⋊ D127⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C127 | C2×C7 |
| LCS | G ▷ C13×C127 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1651 |
Polycyclic presentation:
2,7,13,127|c^a=c^12,d^a=d^126,d^b=d^4173 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23114, 12);