Finite Group DatabasebetaFinite Group Databasebeta| order | 22724 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C19⋊#261 |
| unambiguous semidirect product | C19⋊(C23×#261) |
| Fitting, socle, Hall | C13×C19×C23 ⋊ C4 |
| derived, Hall | C13×C19 ⋊ C4×C23 |
| Hall | C19×C23 ⋊ #261 |
| Hall | C13×C23 ⋊ Dic19 |
| Sylow | C19 ⋊ C23×#261 |
| Sylow | C13 ⋊ C23×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C19⋊#261 |
| commutator, hypocenter | C13×C19 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C13×C19×C23 | C4 |
| prime radical | C19×C23×D13 | C2 |
| cosocle | C19×D13 | C2×C23 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5681 |
1817 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22724, 13);