Finite Group DatabasebetaFinite Group Databasebeta| order | 33524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C2 |
| direct product | C2×C29×D289 |
| unambiguous semidirect product | C289⋊(C22×C29) |
| unambiguous semidirect product | (C2×C289)⋊(C2×C29) |
| Fitting | C2×C29×C289 ⋊ C2 |
| derived, Sylow | C289 ⋊ C22×C29 |
| Hall | C29×C289 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | D289 |
| commutator, cosocle, hypocenter | C289 | C22×C29 |
| Frattini | C17 | C2×C29×D17 |
| Fitting | C2×C29×C289 | C2 |
| socle | C2×C17×C29 | D17 |
| LCS | G ▷ C289 | |
| UCS | C1 ◁ C2×C29 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16762 |
8468 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33524, 14);