Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C2×C33×C8 ⋊ C22 |
| Sylow | C33 ⋊ #407 |
1340 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|c^2=d,d^2=f,c^a=cf,g^a=g^2,h^a=h^2,c^b=ce,i^b=i^2192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 26090);