G:=SmallGroup(32,42);

Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1
        Id(G)

[2]     Order 2       Length 1
        G.5

[3]     Order 2       Length 2
        G.3 * G.4

[4]     Order 2       Length 4
        G.2

[5]     Order 2       Length 4
        G.1

[6]     Order 4       Length 1
        G.3 * G.5

[7]     Order 4       Length 1
        G.3

[8]     Order 4       Length 2
        G.4

[9]     Order 4       Length 4
        G.1 * G.3

[10]    Order 4       Length 4
        G.2 * G.3

[11]    Order 8       Length 2
        G.1 * G.2 * G.3 * G.5

[12]    Order 8       Length 2
        G.1 * G.2 * G.3

[13]    Order 8       Length 2
        G.1 * G.2 * G.5

[14]    Order 8       Length 2
        G.1 * G.2




Character Table of Group G
--------------------------


----------------------------------------------------------
Class |   1  2  3  4  5    6    7  8  9 10  11  12  13  14
Size  |   1  1  2  4  4    1    1  2  4  4   2   2   2   2
Order |   1  2  2  2  2    4    4  4  4  4   8   8   8   8
----------------------------------------------------------
p  =  2   1  1  1  1  1    2    2  2  2  2   8   8   8   8
----------------------------------------------------------
X.1   +   1  1  1  1  1    1    1  1  1  1   1   1   1   1
X.2   +   1  1  1  1 -1    1    1  1 -1  1  -1  -1  -1  -1
X.3   +   1  1 -1  1  1   -1   -1  1 -1 -1  -1  -1   1   1
X.4   +   1  1 -1  1 -1   -1   -1  1  1 -1   1   1  -1  -1
X.5   +   1  1 -1 -1  1   -1   -1  1 -1  1   1   1  -1  -1
X.6   +   1  1 -1 -1 -1   -1   -1  1  1  1  -1  -1   1   1
X.7   +   1  1  1 -1  1    1    1  1  1 -1  -1  -1  -1  -1
X.8   +   1  1  1 -1 -1    1    1  1 -1 -1   1   1   1   1
X.9   +   2  2 -2  0  0    2    2 -2  0  0   0   0   0   0
X.10  +   2  2  2  0  0   -2   -2 -2  0  0   0   0   0   0
X.11  0   2 -2  0  0  0 -2*I  2*I  0  0  0  Z1 -Z1  Z2 -Z2
X.12  0   2 -2  0  0  0 -2*I  2*I  0  0  0 -Z1  Z1 -Z2  Z2
X.13  0   2 -2  0  0  0  2*I -2*I  0  0  0 -Z1  Z1  Z2 -Z2
X.14  0   2 -2  0  0  0  2*I -2*I  0  0  0  Z1 -Z1 -Z2  Z2


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

# denotes algebraic conjugation, that is,
#k indicates replacing the root of unity w by w^k

I = RootOfUnity(4)

Z1     = (CyclotomicField(8: Sparse := true)) ! [ RationalField() | 0, -1, 0, -1 ]
Z2     = (CyclotomicField(8: Sparse := true)) ! [ RationalField() | 0, -1, 0, 1 ]