1.(a)The table below is a partial character tableof a finite group in which a = (-1+ i/3)2and ß =1(-1+ iv7). The conjugacy2%3Dclasses are all shown.(1)(3)(3)(7)(7)X1111a3BX33B(i)Determine the order of the group, thenumber of irreducible representationsand their dimensions.(ii) Determiņe the remaining characters.18

(i) As we completed the character table below from that we get there are 5 conjugacy classes. And…

Ca) The table below is a partial character table of a finite group in which a = 2 ;(-1+ iv3) and B 1 (-1+ iv7). The conjugacy = classes are all shown. (1) (3) (3) (7) (7) X1 1 1 1 a X2 3 B X3 3 (i) Determine the order of the group, the number of irreducible representations and their dimensions. (ii) Determine the remaining characters. 18

Ca) The table below is a partial character table of a finite group in which a = 2 ;(-1+ iv3) and B 1 (-1+ iv7). The conjugacy = classes are all shown. (1) (3) (3) (7) (7) X1 1 1 1 a X2 3 B X3 3 (i) Determine the order of the group, the number of irreducible representations and their dimensions. (ii) Determine the remaining characters. 18

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 2E: 2. Show that is a normal subgroup of the multiplicative group of invertible matrices in .

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Question

1.
(a)
The table below is a partial character table
of a finite group in which a = (-1+ i/3)
2
and ß =
1
(-1+ iv7). The conjugacy
2
%3D
classes are all shown.
(1)
(3)
(3)
(7)
(7)
X1
1
1
1
a
3
B
X3
3
B
(i)
Determine the order of the group, the
number of irreducible representations
and their dimensions.
(ii) Determiņe the remaining characters.
18

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