Finite Group DatabasebetaFinite Group Databasebeta| order | 33374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D407 |
| unambiguous semidirect product | C11⋊(C41×D37) |
| unambiguous semidirect product | C37⋊(D11×C41) |
| Fitting, socle, Hall | C11×C37×C41 ⋊ C2 |
| derived, Hall | C11×C37 ⋊ C2×C41 |
| Hall | C37×C41 ⋊ D11 |
| Hall | C11×C41 ⋊ D37 |
| Sylow | C37 ⋊ D11×C41 |
| Sylow | C11 ⋊ C41×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D407 |
| commutator, cosocle, hypocenter | C11×C37 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C11×C37×C41 | C2 |
| LCS | G ▷ C11×C37 | |
| UCS | C1 ◁ C41 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16687 |
8405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33374, 7);