Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C3×C4×D4×C3⋊D3 |
| Fitting | C33×C4×D4 ⋊ C2 |
| Sylow | C33 ⋊ C2×C4×D4 |
2932 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C3⋊D3×#442, C4×D3×D4×C3⋊D3, C3⋊D3×#5014, … |
| maximal normal subgroup of | C3×C3⋊D3×#442, C4×D3×D4×C3⋊D3, C3⋊D3×#5014 |
| maximal quotient of | C3×C3⋊D3×#442, C4×D4×C3⋊AGL(1,ℤ/9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45360);