Finite Group DatabasebetaFinite Group Databasebeta| order | 24388 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C67⋊#261 |
| unambiguous semidirect product | C67⋊(C7×#261) |
| Fitting, socle, Hall | C7×C13×C67 ⋊ C4 |
| derived, Hall | C13×C67 ⋊ C4×C7 |
| Hall | C7×C67 ⋊ #261 |
| Hall | C7×C13 ⋊ Dic67 |
| Sylow | C67 ⋊ C7×#261 |
| Sylow | C13 ⋊ C7×Dic67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C67⋊#261 |
| commutator, hypocenter | C13×C67 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C67 | C4 |
| prime radical | C7×D13×C67 | C2 |
| cosocle | D13×C67 | C2×C7 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6097 |
1897 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24388, 11);