Finite Group DatabasebetaFinite Group Databasebeta| order | 32465 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×C151⋊C5 |
| unambiguous semidirect product | C151⋊(C5×C43) |
| unambiguous semidirect product | (C43×C151)⋊C5 |
| Fitting, socle, Hall | C43×C151 ⋊ C5 |
| derived, Sylow | C151 ⋊ C5×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C151⋊C5 |
| commutator, cosocle, hypocenter | C151 | C5×C43 |
| Frattini | C1 | G |
| Fitting, socle | C43×C151 | C5 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C43 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6493 |
1505 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32465, 1);