Finite Group DatabasebetaFinite Group Databasebeta| order | 32499 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C23 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C23×C157 ⋊ C3 |
| derived, Sylow | C157 ⋊ C32×C23 |
| Hall | C23×C157 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | C157⋊C3 |
| commutator, cosocle, hypocenter | C157 | C32×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C157 | C3 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C3×C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10833 |
3795 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32499, 4);