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
Section4.4: Cosets Of A Subgroup
Problem 24E: Find two groups of order 6 that are not isomorphic.
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Transcribed Image Text: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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