Finite Group DatabasebetaFinite Group Databasebeta| order | 32085 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9×C23 · Schur multiplier (H2) = C1 |
| direct product | C5×C23×C31⋊C9 |
| unambiguous semidirect product | (C5×C31)⋊(C9×C23) |
| unambiguous semidirect product | (C5×C23×C31)⋊C9 |
| derived, Sylow | C31 ⋊ C5×C9×C23 |
| Hall | C5×C23×C31 ⋊ C9 |
| Hall | C23×C31 ⋊ C5×C9 |
| Hall | C5×C31 ⋊ C9×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C23 | C31⋊C3 |
| commutator, hypocenter | C31 | C5×C9×C23 |
| Frattini | C3 | C5×C23×C31⋊C3 |
| Fitting, socle, prime radical | C3×C5×C23×C31 | C3 |
| cosocle | C3×C31 | C3×C5×C23 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C5×C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32085 |
4485 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32085, 3);