Finite Group DatabasebetaFinite Group Databasebeta| order | 23556 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C22×#20238113 |
| Fitting, socle, Hall | C22×C13×C151 ⋊ C3 |
| derived, Hall | C13×C151 ⋊ C22×C3 |
| Hall | C22×C151 ⋊ C13⋊C3 |
| Sylow | C151 ⋊ C22×C13⋊C3 |
| Hall | C22×C13 ⋊ C151⋊C3 |
| Sylow | C13 ⋊ C22×C151⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #20238113 |
| commutator, cosocle, hypocenter | C13×C151 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C13×C151 | C3 |
| LCS | G ▷ C13×C151 | |
| UCS | C1 ◁ C22 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7852 |
2628 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23556, 68);