Finite Group DatabasebetaFinite Group Databasebeta| order | 22971 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×#10625203 |
| Fitting, socle, Hall | C13×C19×C31 ⋊ C3 |
| derived, Hall | C13×C19 ⋊ C3×C31 |
| Hall | C19×C31 ⋊ C13⋊C3 |
| Hall | C13×C31 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ C31×C13⋊C3 |
| Sylow | C13 ⋊ C31×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #10625203 |
| commutator, cosocle, hypocenter | C13×C19 | C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C13×C19×C31 | C3 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C31 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7657 |
2635 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22971, 12);