Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C22 |
| direct product | C2×D3×C22⋊C27 |
| unambiguous semidirect product | C3⋊(C22×C22⋊C27) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C22⋊C27) |
| unambiguous semidirect product | (C23×D3)⋊C27 |
| derived | C22×C3 ⋊ C22×C27 |
214 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1845);