Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of A4×(C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | A4×(C3⋊Dic3)⋊C3 |
| unambiguous semidirect product | ((C3⋊Dic3)⋊A4)⋊C3 |
| unambiguous semidirect product | (C22×(C3⋊Dic3)⋊C3)⋊C3 |
| unambiguous semidirect product | (A4×C3⋊Dic3)⋊C3 |
| derived | C22×C32 ⋊ C32×C4 |
249 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #72242698, C4×A4×(C3⋊D3)⋊C3 |
| maximal normal subgroup of | C4×A4×(C3⋊D3)⋊C3 |
| maximal quotient of | #72242698 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2160);