Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of ((C22⋊C9)⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C4×((C22⋊C9)⋊C2)⋊C3 |
| unambiguous semidirect product | ((C22⋊C9)⋊C2)⋊(C2×C3×C4) |
| unambiguous semidirect product | (C2×C4×(C22⋊C9)⋊C2)⋊C3 |
| derived | C22⋊C9 ⋊ C22×C3×C4 |
874 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#63694⋊C3 |
| maximal normal subgroup of | C4×#63694⋊C3 |
| maximal quotient of | C4×#63694⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30452);