Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of D3×C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C4 |
| direct product | C3×Dic3×C42⋊C3 |
| unambiguous semidirect product | C3⋊(C3×C4×C42⋊C3) |
| unambiguous semidirect product | (C42×Dic3)⋊C32 |
| unambiguous semidirect product | (C3×C42×Dic3)⋊C3 |
| derived | C3×C42 ⋊ C32×C4 |
332 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 23092);