Finite Group DatabasebetaFinite Group Databasebeta| order | 32499 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C157⋊C9 |
| unambiguous semidirect product | C157⋊(C9×C23) |
| unambiguous semidirect product | (C23×C157)⋊C9 |
| derived, Sylow | C157 ⋊ C9×C23 |
| Hall | C23×C157 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | C157⋊C3 |
| commutator, hypocenter | C157 | C9×C23 |
| Frattini | C3 | C23×C157⋊C3 |
| Fitting, socle, prime radical | C3×C23×C157 | C3 |
| cosocle | C3×C157 | C3×C23 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C3×C23 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32499 |
3795 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32499, 2);