Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic3×C9⋊A4 |
| unambiguous semidirect product | C3⋊(C4×C9⋊A4) |
| unambiguous semidirect product | (C9×Dic3)⋊A4 |
190 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2159);