Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊((C27⋊C3)⋊C4) |
| unambiguous semidirect product | (C4⋊Dic27)⋊C3 |
| Sylow | C27⋊C3 ⋊ C4⋊C4 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^2,3,2^2,3^3|a^2=e,b^2=d,f^3=g,g^3=h,b^a=bd,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,f^c=fh150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 343);