Finite Group DatabasebetaFinite Group Databasebeta| order | 32391 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×C61⋊C9 |
| unambiguous semidirect product | C61⋊(C9×C59) |
| unambiguous semidirect product | (C59×C61)⋊C9 |
| derived, Sylow | C61 ⋊ C9×C59 |
| Hall | C59×C61 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C59 | C61⋊C3 |
| commutator, hypocenter | C61 | C9×C59 |
| Frattini | C3 | C59×C61⋊C3 |
| Fitting, socle, prime radical | C3×C59×C61 | C3 |
| cosocle | C3×C61 | C3×C59 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3×C59 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32391 |
4071 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32391, 2);