Finite Group DatabasebetaFinite Group Databasebeta| order | 33524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C17 |
| direct product | C2×C17⋊D493 |
| unambiguous semidirect product | (C2×C17)⋊D493 |
| unambiguous semidirect product | (C2×C29)⋊(C17⋊D17) |
| Fitting, socle | C2×C172×C29 ⋊ C2 |
| derived, Hall | C172×C29 ⋊ C22 |
| Sylow | C172 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×C17⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C17⋊D493 |
| commutator, cosocle, hypocenter | C172×C29 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C172×C29 | C2 |
| LCS | G ▷ C172×C29 | |
| UCS | C1 ◁ C2 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16762 |
8384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33524, 50);