Finite Group DatabasebetaFinite Group Databasebeta| order | 32679 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C3631⋊C3 |
| unambiguous semidirect product | C3631⋊C32 |
| unambiguous semidirect product | (C3×C3631)⋊C3 |
| Fitting, socle | C3×C3631 ⋊ C3 |
| derived, Sylow | C3631 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3631⋊C3 |
| commutator, cosocle, hypocenter | C3631 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C3631 | C3 |
| LCS | G ▷ C3631 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10893 |
3639 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32679, 3);