Finite Group DatabasebetaFinite Group Databasebeta| order | 33785 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C29 · Schur multiplier (H2) = C1 |
| direct product | C5×C233⋊C29 |
| unambiguous semidirect product | C233⋊(C5×C29) |
| unambiguous semidirect product | (C5×C233)⋊C29 |
| Fitting, socle, Hall | C5×C233 ⋊ C29 |
| derived, Sylow | C233 ⋊ C5×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C233⋊C29 |
| commutator, cosocle, hypocenter | C233 | C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C5×C233 | C29 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1165 |
185 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33785, 1);