Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#20266588 |
| derived, Hall | #15692430 ⋊ C2×C5 |
| Hall | C5×#15692430 ⋊ C2 |
| Hall | C5×C192 ⋊ D9 |
| Sylow | C192 ⋊ C5×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #20266588 |
| commutator, cosocle, hypocenter | #15692430 | C2×C5 |
| Frattini | C3 | C5×#14524212 |
| Fitting, socle | C3×C5×C192 | D3 |
| LCS | G ▷ #15692430 | |
| UCS | C1 ◁ C5 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 855 |
1065 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 53);