Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of D9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C4×D9⋊A4 |
| unambiguous semidirect product | D9⋊(C2×C4×A4) |
| unambiguous semidirect product | (C2×C4×D9)⋊A4 |
| Fitting | C23×C4×C9 ⋊ C2×C3 |
| derived | C22×C9 ⋊ C22×C3×C4 |
967 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 967 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30627);