Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (#611⋊C3)⋊C8 |
| unambiguous semidirect product | (#611⋊C8)⋊C3 |
| Fitting | 3−1+2×C22⋊C8 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C8×D4 |
427 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^3,3,2^3,3^2|c^2=e,e^2=g,h^3=i,b^a=bf,h^a=h^2i^2,i^a=i^2,c^b=cf,h^d=hi^2200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7695);