type 
P(k) = 1 
wallpaper type of kernel group, with remarks 
pmm

none 
pmm, same as the extended group 
pm'm'

M 
p2, all mirrors negating 
pmm'

R 
pm = {t_{1}, t_{2}, M},
one negating mirror 

R and M 
same as above,
i(M) = M R 
p'_{b}mm

t_{1} (t_{2}) 
pmm = {t_{1}, t_{2}^{2}, M}


t_{2} and M 
same as above,
i(M) = M t_{2} 

R and t_{1} (t_{2}) 
same as above,
i(R) = R t_{1} 

R, M and t_{1} (t_{2}) 
same as above,
i(R) = R t_{1}, i(M) =
M t_{1} 
p'_{b}gm

t_{1} and M 
pmg = {t_{2}, R, t_{1}^{2} M};
doubled cell 
c'mm

t_{1} and t_{2} 
cmm = {t_{1} t_{2}, R, M};
doubled cell 

M, t_{1} and t_{2} 
same as above,
i(M) = M t_{2} 

R, t_{1} and t_{2} 
same as above,
i(R) = R t_{1} 

R, M, t_{1} and t_{2} 
same as above,
i(R) = R t_{1},
i(M) = M t_{1} 