Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2 |
| direct product | 3−1+2×A5 |
| unambiguous semidirect product | C9⋊(C3×A5) |
| unambiguous semidirect product | (C9×A5)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C3 | C32×A5 |
| commutator, socle | C3×A5 | C32 |
| Fitting, hypercenter | 3−1+2 | A5 |
| prime radical | C32×A5 | C3 |
| hypocenter | A5 | 3−1+2 |
| LCS | G ▷ C3×A5 ▷ A5 | |
| UCS | C1 ◁ C3 ◁ 3−1+2 | |
105 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
55 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 264);