Finite Group DatabasebetaFinite Group Databasebeta| order | 30682 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C529 · Schur multiplier (H2) = C1 |
| direct product | D29×C529 |
| unambiguous semidirect product | C29⋊(C2×C529) |
| Fitting, Hall | C29×C529 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C529 | D29 |
| commutator, hypocenter | C29 | C2×C529 |
| Frattini | C23 | C23×D29 |
| Fitting | C29×C529 | C2 |
| socle, cosocle | C23×C29 | C2×C23 |
| prime radical | C23×D29 | C23 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C529 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15341 |
8464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30682, 3);