Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×D8×C3⋊D9 |
| Fitting | C2×C3×C9×D8 ⋊ C2 |
| Sylow | C3×C9 ⋊ C22×D8 |
1690 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D9×#442, C2×D8×C9⋊D9, C2×AGL(1,ℤ/8)×C3⋊D9, … |
| maximal normal subgroup of | C3⋊D9×#442, C2×AGL(1,ℤ/8)×C3⋊D9, C2×D8×C3⋊AGL(1,ℤ/9) |
| maximal quotient of | C2×D8×C9⋊D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 20404);