Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×D3×#833 |
| Sylow | C33 ⋊ C2×#100 |
1126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#5077, D3×#10591510, D3×#10591503 |
| maximal normal subgroup of | C3×D3×#5077, D3×#10591510, D3×#10591503 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 24576);