Finite Group DatabasebetaFinite Group Databasebeta| order | 22724 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×Dic299 |
| unambiguous semidirect product | C23⋊(C19×Dic13) |
| derived, Hall | C13×C23 ⋊ C4×C19 |
| Hall | C13×C19×C23 ⋊ C4 |
| Hall | C19×C23 ⋊ Dic13 |
| Hall | C13×C19 ⋊ Dic23 |
| Sylow | C23 ⋊ C19×Dic13 |
| Sylow | C13 ⋊ C19×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D299 |
| commutator, hypocenter | C13×C23 | C4×C19 |
| Frattini | C2 | C19×D299 |
| Fitting, socle, prime radical | C2×C13×C19×C23 | C2 |
| cosocle | C2×C13×C23 | C2×C19 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 ◁ C2×C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22724 |
5738 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22724, 6);