Finite Group DatabasebetaFinite Group Databasebeta| order | 22971 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#13183714 |
| Fitting, socle, Hall | C13×C19×C31 ⋊ C3 |
| derived, Hall | C19×C31 ⋊ C3×C13 |
| Hall | C13×C31 ⋊ C19⋊C3 |
| Hall | C13×C19 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ C13×C19⋊C3 |
| Sylow | C19 ⋊ C13×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #13183714 |
| commutator, cosocle, hypocenter | C19×C31 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C19×C31 | C3 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7657 |
2587 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22971, 5);