G:=SmallGroup(16,6); Conjugacy Classes of group G ---------------------------- [1] Order 1 Length 1 Id(G) [2] Order 2 Length 1 G.4 [3] Order 2 Length 2 G.2 [4] Order 4 Length 1 G.3 * G.4 [5] Order 4 Length 1 G.3 [6] Order 4 Length 2 G.2 * G.3 [7] Order 8 Length 2 G.1 * G.3 [8] Order 8 Length 2 G.1 * G.2 * G.3 [9] Order 8 Length 2 G.1 * G.2 [10] Order 8 Length 2 G.1 Character Table of Group G -------------------------- ------------------------------------------ Class | 1 2 3 4 5 6 7 8 9 10 Size | 1 1 2 1 1 2 2 2 2 2 Order | 1 2 2 4 4 4 8 8 8 8 ------------------------------------------ p = 2 1 1 1 2 2 2 4 5 4 5 ------------------------------------------ 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 0 1 1 -1 -1 -1 1 I -I I -I X.6 0 1 1 1 -1 -1 -1 I I -I -I X.7 0 1 1 -1 -1 -1 1 -I I -I I X.8 0 1 1 1 -1 -1 -1 -I -I I I X.9 0 2 -2 0 2*I -2*I 0 0 0 0 0 X.10 0 2 -2 0 -2*I 2*I 0 0 0 0 0 Explanation of Character Value Symbols -------------------------------------- I = RootOfUnity(4)