Finite Group DatabasebetaFinite Group Databasebeta| order | 22724 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×D13×D23 |
| unambiguous semidirect product | (C23×D13)⋊(C2×C19) |
| unambiguous semidirect product | (C13×D23)⋊(C2×C19) |
| unambiguous semidirect product | D299⋊(C2×C19) |
| Fitting, socle, Hall | C13×C19×C23 ⋊ C22 |
| derived, Hall | C13×C23 ⋊ C22×C19 |
| Hall | C19×C23 ⋊ C2×D13 |
| Hall | C13×C19 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C19×D13 |
| Sylow | C13 ⋊ C2×C19×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D13×D23 |
| commutator, cosocle, hypocenter | C13×C23 | C22×C19 |
| Frattini | C1 | G |
| Fitting, socle | C13×C19×C23 | C22 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 ◁ C19 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5681 |
1976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22724, 15);