Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C3 |
| direct product | D4×(C3⋊S4)⋊C3 |
| unambiguous semidirect product | (D4×C3⋊S4)⋊C3 |
| Fitting | C22×C32×D4 ⋊ D3 |
948 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
95 conjugacy classes — view the full character table.
| maximal subgroup of | #67×(C3⋊S4)⋊C3, S4×(C3⋊S4)⋊C3, D4×((C3⋊S4)⋊C3)⋊C2 |
| maximal normal subgroup of | D4×((C3⋊S4)⋊C3)⋊C2 |
| maximal quotient of | #67×(C3⋊S4)⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30465);