Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| unambiguous semidirect product | #10592520⋊C3 |
| Fitting | H(3,𝔽3)×#104 ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #421 |
583 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^3,3,2^3,3^2|c^2=e,e^2=g,f^2=g,c^a=cg,h^a=h^2,i^a=i^2,c^b=cf,f^b=fg,f^c=fg,h^d=hi122 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 8044);