Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C9 · Schur multiplier (H2) = C22×C33 |
| direct product | C22×C3×C9×A4 |
| Fitting | C24×C3×C9 ⋊ C3 |
| derived | C22 ⋊ C22×C32×C9 |
| Sylow | C24 ⋊ C32×C9 |
690 conjugacy classes of subgroups; only the 300 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 300 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3042);