Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3×C27 ⋊ SD16 |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^4,3^4|b^2=d,c^2=d,f^3=g,g^3=h,b^a=bc,c^a=cd,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,c^b=cd,e^b=e^2129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 123);