Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C3×D3×D4×A4 |
| unambiguous semidirect product | (C22×D3×D4)⋊C32 |
| unambiguous semidirect product | (C22×C3×D3×D4)⋊C3 |
| Fitting | C22×C32×D4 ⋊ C2×C3 |
1646 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×A4×S4, C3×D3×D4×S4, D32×D4×A4, … |
| maximal normal subgroup of | C3×D3×D4×S4, D32×D4×A4, D3×D4×C3⋊S4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47502);