Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #611⋊(C3⋊C8) |
| Sylow | C3×C9 ⋊ C8×D4 |
478 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|b^2=e,e^2=f,g^3=i,c^a=cd,g^a=g^2i^2,i^a=i^2,c^b=cd,h^b=h^2204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 5548);