Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | ((C3⋊D3)⋊C3)⋊#95 |
| Sylow | H(3,𝔽3) ⋊ C2×#95 |
1231 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|b^2=f,c^2=d,g^a=g^2,i^a=i^2,c^b=ce,h^b=h^2,i^b=i^2,h^g=hi128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 6295);