Finite Group DatabasebetaFinite Group Databasebeta| order | 36020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C22×C1801⋊C5 |
| unambiguous semidirect product | (C22×C1801)⋊C5 |
| Fitting, socle, Hall | C22×C1801 ⋊ C5 |
| derived, Sylow | C1801 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C1801⋊C5 |
| commutator, cosocle, hypocenter | C1801 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C1801 | C5 |
| LCS | G ▷ C1801 | |
| UCS | C1 ◁ C22 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7204 |
1460 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36020, 10);