Jim Caprioli at The Finland Station

After having played with Z4x|Z4 for four consecutive days, I gave up on finding the last two characters. I peeked in GAP's library:

gap> List(AllGroups(16),StructureDescription);
[ "C16", "C4 x C4", "(C4 x C2) : C2", "C4 : C4", "C8 x C2", "C8 : C2", "D16",
"QD16", "Q16", "C4 x C2 x C2", "C2 x D8", "C2 x Q8", "(C4 x C2) : C2",
"C2 x C2 x C2 x C2" ]
gap> G:=AllGroups(16)[4];
<pc group of size 16 with 4 generators>
gap>; StructureDescription(G);
"C4 : C4"
gap> Display(CharacterTable(G));
CT5

2 4 3 3 4 4 3 3 3 4 3

1a 4a 4b 2a 2b 4c 4d 4e 2c 4f
2P 1a 2b 2a 1a 1a 2b 2b 2a 1a 2b
3P 1a 4d 4b 2a 2b 4f 4a 4e 2c 4c

X.1 1 1 1 1 1 1 1 1 1 1
X.2 1 -1 -1 1 1 1 -1 -1 1 1
X.3 1 -1 1 1 1 -1 -1 1 1 -1
X.4 1 1 -1 1 1 -1 1 -1 1 -1
X.5 1 A -1 1 -1 -A -A 1 -1 A
X.6 1 -A -1 1 -1 A A 1 -1 -A
X.7 1 A 1 1 -1 A -A -1 -1 -A
X.8 1 -A 1 1 -1 -A A -1 -1 A
X.9 2 . . -2 2 . . . -2 .
X.10 2 . . -2 -2 . . . 2 .

A = -E(4)
= -ER(-1) = -i

Goals for the forthcoming period
- Why?! wasn't I able to construct these damned representations?!
- Reconstruct and analyze the representations as in X.9 and X.10;
- Write a summary of the theory which has been studied sofar;
- Repeat this exercise for the group C3 x| Q8. (Non-Abelian, Order=24);