Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D3×#63883 |
| Sylow | C33 ⋊ C22×C4⋊C4 |
2146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#3811 |
| maximal normal subgroup of | C4×D3×#3811 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 36771);