Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C4×D4×C3⋊D9 |
| Fitting | C3×C4×D4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×C4×D4 |
2130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D9×#442, C4×D4×C9⋊D9, C4×D4×C3⋊AGL(1,ℤ/9) |
| maximal normal subgroup of | C3⋊D9×#442, C4×D4×C3⋊AGL(1,ℤ/9) |
| maximal quotient of | C3⋊D9×#442, C4×D4×C9⋊D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19978);