Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C16 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×C3⋊C16 |
| unambiguous semidirect product | C3⋊(C3×A4×C16) |
| unambiguous semidirect product | (C22×C3⋊C16)⋊C32 |
| unambiguous semidirect product | (C22×C3×C3⋊C16)⋊C3 |
| derived | C22×C3 ⋊ C32×C16 |
246 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 23096);