Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic81⋊C4 |
| Sylow | C81 ⋊ C4⋊C4 |
65 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1296 |
Polycyclic presentation:
2^4,3^4|a^2=d,b^2=c,e^3=f,f^3=g,g^3=h,b^a=bd,e^a=e^2f^2g^2h^2,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2330 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 12);