Finite Group DatabasebetaFinite Group Databasebeta| order | 33748 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C59⋊#261 |
| unambiguous semidirect product | C59⋊(C11×#261) |
| Fitting, socle, Hall | C11×C13×C59 ⋊ C4 |
| derived, Hall | C13×C59 ⋊ C4×C11 |
| Hall | C11×C59 ⋊ #261 |
| Hall | C11×C13 ⋊ Dic59 |
| Sylow | C59 ⋊ C11×#261 |
| Sylow | C13 ⋊ C11×Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C59⋊#261 |
| commutator, hypocenter | C13×C59 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C59 | C4 |
| prime radical | C11×D13×C59 | C2 |
| cosocle | D13×C59 | C2×C11 |
| LCS | G ▷ C13×C59 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8437 |
2629 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33748, 11);