Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×#4700 |
| Fitting | C3×C4×C8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ #443 |
362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7504);