Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×D3×D4×D9 |
| Fitting | C2×C3×D4×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C23×D4 |
4322 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13164733, C2×D4×D92, D3×D9×#127, … |
| maximal normal subgroup of | C2×#13164733, D3×D9×#127, D3×D9×#120 |
| maximal quotient of | C2×D4×D92, D3×D9×#127, C2×D4×D9×C3⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30790);