Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C2 |
| direct product | C27×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C27 | A5 |
| commutator, hypocenter | A5 | C27 |
| Frattini, cosocle | C9 | C3×A5 |
| socle, prime radical | C3×A5 | C9 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C27 | |
45 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 71);