Finite Group DatabasebetaFinite Group Databasebeta| order | 32420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20266483⋊C5 |
| Fitting, socle, derived, Sylow | C1621 ⋊ C4×C5 |
| Hall | C1621⋊C5 ⋊ C4 |
| Hall | #20266483 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1621 | C4×C5 |
| prime radical | D1621⋊C5 | C2 |
| cosocle | D1621 | C2×C5 |
| LCS | G ▷ C1621 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1621 |
Polycyclic presentation:
2,5,2,1621|a^2=c,d^a=d^166,d^b=d^1489,d^c=d^1620101 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32420, 8);