Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of A4×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C4×A4×C3⋊D3 |
| Fitting | C23×C32×C4 ⋊ C2×C3 |
| derived | C22×C32 ⋊ C22×C3×C4 |
2030 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 2030 conjugacy classes of subgroups — too many to draw. Only its 201 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47520);