Finite Group DatabasebetaFinite Group Databasebeta| order | 32679 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3631⋊C9 |
| derived, Sylow | C3631 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C3631⋊C3 |
| commutator, hypocenter | C3631 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C3631 | C3 |
| LCS | G ▷ C3631 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32679 |
Polycyclic presentation:
3^2,3631|a^3=b,c^a=c^32953639 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32679, 1);