Finite Group DatabasebetaFinite Group Databasebeta| order | 30627 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C41 · Schur multiplier (H2) = C1 |
| direct product | C9×C83⋊C41 |
| unambiguous semidirect product | C83⋊(C9×C41) |
| unambiguous semidirect product | (C9×C83)⋊C41 |
| Fitting, Hall | C9×C83 ⋊ C41 |
| derived, Sylow | C83 ⋊ C9×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C83⋊C41 |
| commutator, hypocenter | C83 | C9×C41 |
| Frattini | C3 | C3×C83⋊C41 |
| Fitting | C9×C83 | C41 |
| socle, cosocle | C3×C83 | C3×C41 |
| prime radical | C3×C83⋊C41 | C3 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 747 |
387 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30627, 2);