Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×C3×C4×D32 |
| Fitting | C22×C33×C4 ⋊ C22 |
| derived | C32 ⋊ C24×C3×C4 |
| Sylow | C33 ⋊ C24×C4 |
6210 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47600);