Finite Group DatabasebetaFinite Group Databasebeta| order | 33350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D725 |
| unambiguous semidirect product | C25⋊(C23×D29) |
| unambiguous semidirect product | C29⋊(C23×D25) |
| Fitting, Hall | C23×C25×C29 ⋊ C2 |
| derived, Hall | C25×C29 ⋊ C2×C23 |
| Hall | C23×C29 ⋊ D25 |
| Hall | C23×C25 ⋊ D29 |
| Sylow | C29 ⋊ C23×D25 |
| Sylow | C25 ⋊ C23×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D725 |
| commutator, cosocle, hypocenter | C25×C29 | C2×C23 |
| Frattini | C5 | C23×D145 |
| Fitting | C23×C25×C29 | C2 |
| socle | C5×C23×C29 | D5 |
| LCS | G ▷ C25×C29 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16675 |
8372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33350, 6);