Finite Group DatabasebetaFinite Group Databasebeta| order | 33418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D1519 |
| unambiguous semidirect product | C31⋊(C11×D49) |
| unambiguous semidirect product | C49⋊(C11×D31) |
| Fitting, Hall | C11×C31×C49 ⋊ C2 |
| derived, Hall | C31×C49 ⋊ C2×C11 |
| Hall | C11×C49 ⋊ D31 |
| Hall | C11×C31 ⋊ D49 |
| Sylow | C49 ⋊ C11×D31 |
| Sylow | C31 ⋊ C11×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D1519 |
| commutator, cosocle, hypocenter | C31×C49 | C2×C11 |
| Frattini | C7 | C11×D217 |
| Fitting | C11×C31×C49 | C2 |
| socle | C7×C11×C31 | D7 |
| LCS | G ▷ C31×C49 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16709 |
8371 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33418, 6);