Finite Group DatabasebetaFinite Group Databasebeta| order | 33418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D341 |
| unambiguous semidirect product | C11⋊(C49×D31) |
| unambiguous semidirect product | C31⋊(D11×C49) |
| Fitting, Hall | C11×C31×C49 ⋊ C2 |
| derived, Hall | C11×C31 ⋊ C2×C49 |
| Hall | C31×C49 ⋊ D11 |
| Hall | C11×C49 ⋊ D31 |
| Sylow | C31 ⋊ D11×C49 |
| Sylow | C11 ⋊ C49×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D341 |
| commutator, hypocenter | C11×C31 | C2×C49 |
| Frattini | C7 | C7×D341 |
| Fitting | C11×C31×C49 | C2 |
| socle, cosocle | C7×C11×C31 | C2×C7 |
| prime radical | C7×D341 | C7 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C49 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16709 |
8428 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33418, 4);