Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C2×#11722642 |
| Fitting | C2×#41×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C2×2−1+4 |
2464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 31008);