Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | #125×AGL(1,ℤ/9) |
| unambiguous semidirect product | D9⋊(C3×#125) |
| unambiguous semidirect product | (D9×#125)⋊C3 |
| Fitting | 3−1+2×#125 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C2×#125 |
706 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19257);