Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C9 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C42×D3×C9 |
| Fitting | C2×C3×C42×C9 ⋊ C2 |
| derived | C3 ⋊ C22×C42×C9 |
| Sylow | C3×C9 ⋊ C22×C42 |
1602 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
864 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18351);