Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C32×#4711 |
| Fitting | C33×#97 ⋊ C2 |
| Sylow | C33 ⋊ #442 |
952 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×#4711, C32×D3×#442, #72245325 |
| maximal normal subgroup of | C3⋊D3×#4711, C32×D3×#442, #72245325 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 28211);