Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | #4294×D95 |
| unambiguous semidirect product | C5⋊(D19×#4294) |
| derived, Hall | C5×C192 ⋊ C2×C9 |
| Hall | C5×C19×#4294 ⋊ C2 |
| Hall | C19×D95 ⋊ C9 |
| Hall | C19×#4294 ⋊ D5 |
| Sylow | C192 ⋊ C9×D5 |
| Sylow | C5 ⋊ D19×#4294 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C19⋊C3×D95 |
| commutator, hypocenter | C5×C192 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C192 | C2×C3 |
| prime radical | C3×C19×D95 | C3 |
| LCS | G ▷ C5×C192 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1710 |
1323 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 63);