Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#10588397 |
| Fitting | C3×C9×#97 ⋊ C2 |
| Sylow | C3×C9 ⋊ #444 |
352 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7572);