Finite Group DatabasebetaFinite Group Databasebeta| order | 32291 |
| automorphism | ? |
| homology | Abelianization (H1) = C72 · Schur multiplier (H2) = C7 |
| direct product | C7×C659⋊C7 |
| unambiguous semidirect product | C659⋊C72 |
| unambiguous semidirect product | (C7×C659)⋊C7 |
| Fitting, socle | C7×C659 ⋊ C7 |
| derived, Sylow | C659 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C659⋊C7 |
| commutator, cosocle, hypocenter | C659 | C72 |
| Frattini | C1 | G |
| Fitting, socle | C7×C659 | C7 |
| LCS | G ▷ C659 | |
| UCS | C1 ◁ C7 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4613 |
707 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32291, 3);