Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×#733 ⋊ C2 |
| Sylow | #733 ⋊ SD16 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^4,3^4|b^2=d,c^2=d,e^3=h,f^3=h,b^a=bc,c^a=cd,e^a=e^2h^2,f^a=f^2h^2,g^a=gh^2,h^a=h^2,c^b=cd,f^e=fg,g^f=gh56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 550);