Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C5×C192 ⋊ C2×C32 |
| derived, Sylow | C192 ⋊ C2×C32×C5 |
| Hall | C5×C19⋊C32 ⋊ C2 |
| Hall | C5×C19×D19 ⋊ C32 |
| Hall | C19⋊C32 ⋊ C2×C5 |
| Hall | C19×D19 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C19⋊C3×D19⋊C3 |
| commutator, cosocle, hypocenter | C192 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C192 | C2×C32 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C5 | |
108 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 570 |
405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 97);