Finite Group DatabasebetaFinite Group Databasebeta| order | 33572 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C7⋊#89137 |
| unambiguous semidirect product | C7⋊(C11×#89137) |
| Fitting, socle, Hall | C7×C11×C109 ⋊ C4 |
| derived, Hall | C7×C109 ⋊ C4×C11 |
| Hall | C11×C109 ⋊ Dic7 |
| Sylow | C109 ⋊ C11×Dic7 |
| Hall | C7×C11 ⋊ #89137 |
| Sylow | C7 ⋊ C11×#89137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C7⋊#89137 |
| commutator, hypocenter | C7×C109 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C109 | C4 |
| prime radical | C7×C11×D109 | C2 |
| cosocle | C7×D109 | C2×C11 |
| LCS | G ▷ C7×C109 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8393 |
2189 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33572, 13);