Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | #504 ⋊ 3−1+2 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2,3^2,2,3,2^4|a^2=d,b^3=e,d^2=f,f^2=i,g^2=i,h^2=i,c^b=ce,g^b=gh,h^b=g,h^g=hi248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7329);