Finite Group DatabasebetaFinite Group Databasebeta| order | 33524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C289 · Schur multiplier (H2) = C1 |
| direct product | Dic29×C289 |
| derived, Sylow | C29 ⋊ C4×C289 |
| Hall | C29×C289 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C289 | D29 |
| commutator, hypocenter | C29 | C4×C289 |
| Frattini | C2×C17 | C17×D29 |
| Fitting | C2×C29×C289 | C2 |
| socle, prime radical, cosocle | C2×C17×C29 | C2×C17 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C289 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33524 |
9248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33524, 3);