Finite Group DatabasebetaFinite Group Databasebeta| order | 23156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×D827⋊C7 |
| unambiguous semidirect product | D827⋊(C2×C7) |
| unambiguous semidirect product | (C2×D827)⋊C7 |
| unambiguous semidirect product | (C827⋊C7)⋊C22 |
| unambiguous semidirect product | (C2×C827⋊C7)⋊C2 |
| Fitting, socle | C2×C827 ⋊ C2×C7 |
| derived, Sylow | C827 ⋊ C22×C7 |
| Hall | C827⋊C7 ⋊ C22 |
| Hall | C2×D827 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D827⋊C7 |
| commutator, cosocle, hypocenter | C827 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C827 | C2×C7 |
| LCS | G ▷ C827 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1654 |
146 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23156, 8);