Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×D9×#108 |
| Fitting | C3×C9×#108 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×#108 |
348 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 8315);