Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3 |
| direct product | C2×#11723539 |
| Fitting | C22×C33×C4 ⋊ C22 |
| Sylow | C33 ⋊ C22×C22⋊C4 |
4988 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 43353);