Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C9 · Schur multiplier (H2) = C2×C33 |
| direct product | C3×C5×C9×A4 |
| Fitting | C22×C3×C5×C9 ⋊ C3 |
| derived, Sylow | C22 ⋊ C32×C5×C9 |
| Hall | C22×C5 ⋊ C32×C9 |
220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 357);