Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C5×C192 ⋊ C2×C32 |
| Hall | C5×C19⋊C32 ⋊ C2 |
| Hall | D5×C192 ⋊ C32 |
| Sylow | C192 ⋊ C32×D5 |
| Sylow | C5 ⋊ C2×C19⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C192 | C2×C32 |
| LCS | G ▷ C5×C192 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 285 |
324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 123);