Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D1805 |
| unambiguous semidirect product | C5⋊(C32×D361) |
| Fitting, Hall | C32×C5×C361 ⋊ C2 |
| derived, Hall | C5×C361 ⋊ C2×C32 |
| Hall | C32×C361 ⋊ D5 |
| Sylow | C361 ⋊ C32×D5 |
| Hall | C32×C5 ⋊ D361 |
| Sylow | C5 ⋊ C32×D361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D1805 |
| commutator, cosocle, hypocenter | C5×C361 | C2×C32 |
| Frattini | C19 | C32×D95 |
| Fitting | C32×C5×C361 | C2 |
| socle | C32×C5×C19 | D19 |
| LCS | G ▷ C5×C361 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16245 |
8136 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 28);