Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of (C3⋊D3)⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C22×(C3⋊Dic3)⋊A4 |
| derived | C22×C32 ⋊ C22×C3×C4 |
1696 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 1696 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #72242698, C22×C4×(C3⋊D3)⋊A4 |
| maximal normal subgroup of | #72242698, C22×C4×(C3⋊D3)⋊A4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30706);