Finite Group DatabasebetaFinite Group Databasebeta| order | 33418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C7 |
| direct product | C31×C7⋊D77 |
| unambiguous semidirect product | C7⋊(C31×D77) |
| unambiguous semidirect product | C11⋊(C31×C7⋊D7) |
| Fitting, socle, Hall | C72×C11×C31 ⋊ C2 |
| derived, Hall | C72×C11 ⋊ C2×C31 |
| Hall | C72×C31 ⋊ D11 |
| Hall | C11×C31 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D11×C31 |
| Sylow | C11 ⋊ C31×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C7⋊D77 |
| commutator, cosocle, hypocenter | C72×C11 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C72×C11×C31 | C2 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C31 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16709 |
8401 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33418, 19);