Finite Group DatabasebetaFinite Group Databasebeta| order | 32420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C22×C1621⋊C5 |
| unambiguous semidirect product | (C22×C1621)⋊C5 |
| Fitting, socle, Hall | C22×C1621 ⋊ C5 |
| derived, Sylow | C1621 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C1621⋊C5 |
| commutator, cosocle, hypocenter | C1621 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C1621 | C5 |
| LCS | G ▷ C1621 | |
| UCS | C1 ◁ C22 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6484 |
1316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32420, 10);