Jim Caprioli at The Finland Station

Continuing on Z4x|Z4. ( I found out that x| is the preferred ascii notation for semi-direct product on internet although GAP prints the ":" semicolon sign. ) Z4x|Z4 it is. I managed to create a morphism between the constructed Z4x|Z4 and the free group defined by a^4=1, b^4=1 and and b a=a^3 b. This looks better.

Table[{z[[x]],a^z[[x,2]]*b^z[[x,1]]},{x,1,16}]

{
{{0, 0}, 1},
{{0, 1}, a},
{{0, 2}, a^2},
{{0, 3}, a\^3},
{{1, 0}, b},
{{1, 1}, a b},
{{1, 2}, a^2 b},
{{1, 3}, a^3 b},
{{2, 0}, b^2},
{{2, 1}, a b^2},
{{2, 2}, a^2 b^2},
{{2, 3}, a^3 b^2},
{{3, 0}, b^3},
{{3, 1}, a b^3},
{{3, 2}, a^2 b^3},
{{3, 3}, a^3 b^3}
}

I think that I have enough ammunition to start working on the Character Table. We'll see. ( More later. )