Finite Group DatabasebetaFinite Group Databasebeta| order | 33350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C5 |
| direct product | C29×C5⋊D115 |
| unambiguous semidirect product | C5⋊(C29×D115) |
| unambiguous semidirect product | C23⋊(C29×C5⋊D5) |
| Fitting, socle, Hall | C52×C23×C29 ⋊ C2 |
| derived, Hall | C52×C23 ⋊ C2×C29 |
| Hall | C52×C29 ⋊ D23 |
| Hall | C23×C29 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C29×D23 |
| Sylow | C23 ⋊ C29×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C5⋊D115 |
| commutator, cosocle, hypocenter | C52×C23 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C52×C23×C29 | C2 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 ◁ C29 | |
64 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, 19);