Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3×C27 ⋊ Q16 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^4,3^4|a^2=d,b^2=cd,c^2=d,e^3=g,g^3=h,b^a=bc,c^a=cd,f^a=f^2,e^b=e^2g^2h^2,g^b=g^2h^2,h^b=h^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 122);