Finite Group DatabasebetaFinite Group Databasebeta| order | 32641 |
| automorphism | ? |
| homology | Abelianization (H1) = C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C4663⋊C7 |
| Fitting, socle, derived, Sylow | C4663 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C4663 | C7 |
| LCS | G ▷ C4663 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4663 |
Polycyclic presentation:
7,4663|b^a=b^4072673 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32641, 1);