Finite Group DatabasebetaFinite Group Databasebeta| order | 33350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D575 |
| unambiguous semidirect product | C23⋊(C29×D25) |
| unambiguous semidirect product | C25⋊(C29×D23) |
| Fitting, Hall | C23×C25×C29 ⋊ C2 |
| derived, Hall | C23×C25 ⋊ C2×C29 |
| Hall | C25×C29 ⋊ D23 |
| Hall | C23×C29 ⋊ D25 |
| Sylow | C25 ⋊ C29×D23 |
| Sylow | C23 ⋊ C29×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D575 |
| commutator, cosocle, hypocenter | C23×C25 | C2×C29 |
| Frattini | C5 | C29×D115 |
| Fitting | C23×C25×C29 | C2 |
| socle | C5×C23×C29 | D5 |
| LCS | G ▷ C23×C25 | |
| UCS | C1 ◁ C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16675 |
8381 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33350, 7);