Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C3×C4 |
No aliases for this group.
| Sylow | C33 ⋊ C4×C22⋊C4 |
2492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|a^2=f,b^2=ef,c^2=d,b^a=be,c^a=ce,g^a=g^2,h^a=h^2,c^b=ce,i^b=i^2204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 26571);