Finite Group DatabasebetaFinite Group Databasebeta| order | 30566 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D527 |
| unambiguous semidirect product | C17⋊(C29×D31) |
| unambiguous semidirect product | C31⋊(C29×D17) |
| Fitting, socle, Hall | C17×C29×C31 ⋊ C2 |
| derived, Hall | C17×C31 ⋊ C2×C29 |
| Hall | C29×C31 ⋊ D17 |
| Hall | C17×C29 ⋊ D31 |
| Sylow | C31 ⋊ C29×D17 |
| Sylow | C17 ⋊ C29×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D527 |
| commutator, cosocle, hypocenter | C17×C31 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C17×C29×C31 | C2 |
| LCS | G ▷ C17×C31 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15283 |
7685 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30566, 6);