Finite Group DatabasebetaFinite Group Databasebeta| order | 23156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C22×C827⋊C7 |
| unambiguous semidirect product | (C22×C827)⋊C7 |
| Fitting, socle, Hall | C22×C827 ⋊ C7 |
| derived, Sylow | C827 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C827⋊C7 |
| commutator, cosocle, hypocenter | C827 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C827 | C7 |
| LCS | G ▷ C827 | |
| UCS | C1 ◁ C22 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3308 |
500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23156, 9);