Finite Group DatabasebetaFinite Group Databasebeta| order | 32683 |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C23 · Schur multiplier (H2) = C7 |
| Fitting, socle | C7×C23×C29 ⋊ C7 |
| derived, Sylow | C29 ⋊ C72×C23 |
| Hall | C23×C29 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C23 | C29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C72×C23 |
| Frattini | C1 | G |
| Fitting, socle | C7×C23×C29 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C7×C23 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4669 |
1771 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32683, 4);