Finite Group DatabasebetaFinite Group Databasebeta| order | 33524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#14520310 |
| Fitting, socle, Hall | C172×C29 ⋊ C4 |
| derived | C17×C29 ⋊ C4×C17 |
| Sylow | C172 ⋊ #1181 |
| Sylow | C29 ⋊ C17×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #14520310 |
| commutator, hypocenter | C17×C29 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C172×C29 | C4 |
| prime radical | C172×D29 | C2 |
| cosocle | C17×D29 | C2×C17 |
| LCS | G ▷ C17×C29 | |
| UCS | C1 ◁ C17 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 986 |
2363 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33524, 24);