Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #10588229⋊C3 |
| Sylow | 3−1+2 ⋊ #340 |
380 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^2,3,2^4,3^2|a^2=f,b^2=d,d^2=g,e^2=g,h^3=i,b^a=be,d^a=dg,e^a=eg,h^a=h^2i^2,i^a=i^2,h^c=hi^2212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 1722);