Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of (C3⋊D3)⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×(C3⋊(C3⋊C8))⋊A4 |
| unambiguous semidirect product | (C2×C3⋊(C3⋊C8))⋊A4 |
| derived | C22×C32 ⋊ C2×C3×C8 |
480 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 73 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.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13324);