Finite Group DatabasebetaFinite Group Databasebeta| order | 33418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C31 · Schur multiplier (H2) = C1 |
| direct product | C11×C31×D49 |
| unambiguous semidirect product | C49⋊(C2×C11×C31) |
| Fitting, Hall | C11×C31×C49 ⋊ C2 |
| derived, Sylow | C49 ⋊ C2×C11×C31 |
| Hall | C31×C49 ⋊ C2×C11 |
| Hall | C11×C49 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C31 | D49 |
| commutator, cosocle, hypocenter | C49 | C2×C11×C31 |
| Frattini | C7 | C11×D7×C31 |
| Fitting | C11×C31×C49 | C2 |
| socle | C7×C11×C31 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C11×C31 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16709 |
8866 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33418, 5);