Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C9 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×D3×C8×C9 |
| Fitting | C3×C4×C8×C9 ⋊ C2 |
| derived | C3 ⋊ C2×C4×C8×C9 |
| Sylow | C3×C9 ⋊ C2×C4×C8 |
530 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
864 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D3×C7×C8×C9 |
| maximal normal subgroup of | C4×D3×C7×C8×C9 |
| maximal quotient of | C4×D3×C7×C8×C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7488);