Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| unambiguous semidirect product | #10592683⋊C3 |
| Sylow | H(3,𝔽3) ⋊ #389 |
687 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^3,3,2^3,3^2|a^2=g,b^2=f,c^2=f,b^a=bf,c^a=cf,h^a=h^2,i^a=i^2,c^b=ce,h^d=hi164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 8683);