G:=SmallGroup(24,10); 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 2 Length 2 G.1 [5] Order 3 Length 1 G.3^2 [6] Order 3 Length 1 G.3 [7] Order 4 Length 2 G.1 * G.2 * G.4 [8] Order 6 Length 1 G.3 * G.4 [9] Order 6 Length 1 G.3^2 * G.4 [10] Order 6 Length 2 G.2 * G.3 [11] Order 6 Length 2 G.1 * G.3 [12] Order 6 Length 2 G.1 * G.3^2 [13] Order 6 Length 2 G.2 * G.3^2 [14] Order 12 Length 2 G.1 * G.2 * G.3 * G.4 [15] Order 12 Length 2 G.1 * G.2 * G.3^2 * G.4 Character Table of Group G -------------------------- ------------------------------------------------------------------------- Class | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Size | 1 1 2 2 1 1 2 1 1 2 2 2 2 2 2 Order | 1 2 2 2 3 3 4 6 6 6 6 6 6 12 12 ------------------------------------------------------------------------- p = 2 1 1 1 1 6 5 2 5 6 5 5 6 6 9 8 p = 3 1 2 3 4 1 1 7 2 2 3 4 4 3 7 7 ------------------------------------------------------------------------- X.1 + 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 1 X.3 + 1 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 -1 X.5 0 1 1 -1 -1 J -1-J 1 -1-J J 1+J 1+J -J -J-1-J J X.6 0 1 1 1 -1 -1-J J -1 J -1-J J -J 1+J-1-J -J 1+J X.7 0 1 1 -1 -1 -1-J J 1 J -1-J -J -J 1+J 1+J J-1-J X.8 0 1 1 -1 1 J -1-J -1 -1-J J 1+J-1-J J -J 1+J -J X.9 0 1 1 1 1 -1-J J 1 J -1-J J J-1-J-1-J J-1-J X.10 0 1 1 -1 1 -1-J J -1 J -1-J -J J-1-J 1+J -J 1+J X.11 0 1 1 1 -1 J -1-J -1 -1-J J-1-J 1+J -J J 1+J -J X.12 0 1 1 1 1 J -1-J 1 -1-J J-1-J-1-J J J-1-J J X.13 + 2 -2 0 0 2 2 0 -2 -2 0 0 0 0 0 0 X.14 0 2 -2 0 0 -2-2*J 2*J 0 -2*J 2+2*J 0 0 0 0 0 0 X.15 0 2 -2 0 0 2*J -2-2*J 0 2+2*J -2*J 0 0 0 0 0 0 Explanation of Character Value Symbols -------------------------------------- J = RootOfUnity(3)