Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D5×#15692433 |
| unambiguous semidirect product | C5⋊(C2×#15692433) |
| Fitting, socle, derived, Hall | C5×C192 ⋊ C2×C9 |
| Hall | C5×#15692433 ⋊ C2 |
| Hall | D5×C192 ⋊ C9 |
| Sylow | C192 ⋊ C9×D5 |
| Sylow | C5 ⋊ C2×#15692433 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C192 | C2×C9 |
| prime radical | D5×#11762245 | C3 |
| cosocle | C5×#11762245 | C2×C3 |
| LCS | G ▷ C5×C192 | |
| UCS | C1 | |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1805 |
196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 129);