Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32×C8 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C32×D3×C8 |
| Fitting | C22×C33×C8 ⋊ C2 |
| derived | C3 ⋊ C23×C32×C8 |
| Sylow | C33 ⋊ C23×C8 |
2332 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, 45176);