Character Table of Finite Group In Magma

Question

I want to get character table of following group for some $n$ with MAGMA

$$G\langle a,b\rangle := \mathrm{Group}\langle a,b\mid a^{2n}, b^4, b*a*b*a, b^{-1}*a*b^{-1}*a\rangle;$$

Answer 1

You need to convert the group to a more concrete representation, such as a permutation group using PermutationGroup or, if applicable, a finite polycyclic group using PCGroup:

n:=3;
g<a,b>:=Group<a,b| a^(2*n), b^4, b*a*b*a, b^(-1)*a*b^(-1)*a>;
CharacterTable(PCGroup(g));

Character Table
---------------


-----------------------------------------
Class |   1  2  3  4  5  6     7     8  9
Size  |   1  1  2  6  2  6     2     2  2
Order |   1  2  2  2  3  4     6     6  6
-----------------------------------------
p  =  2   1  1  1  1  5  2     5     5  5
p  =  3   1  2  3  4  1  6     3     3  2
-----------------------------------------
X.1   +   1  1  1  1  1  1     1     1  1
X.2   +   1  1  1 -1  1 -1     1     1  1
X.3   +   1  1 -1  1  1 -1    -1    -1  1
X.4   +   1  1 -1 -1  1  1    -1    -1  1
X.5   +   2  2 -2  0 -1  0     1     1 -1
X.6   +   2  2  2  0 -1  0    -1    -1 -1
X.7   +   2 -2  0  0  2  0     0     0 -2
X.8   0   2 -2  0  0 -1  0-1-2*J 1+2*J  1
X.9   0   2 -2  0  0 -1  0 1+2*J-1-2*J  1


Explanation of Character Value Symbols
--------------------------------------

J = RootOfUnity(3)