Projective Representations of Finite Groups by Gregory Karpilovsky

By Gregory Karpilovsky

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2 Structure Character 10 6 Orthogona1 (2) 1a+5a N(5AB) 1a+4a+S a N(3A) Linear (5) isotropic point Linear (4) Orthogona1 (4) point point isotropic point °2 (4), L1(16) minus line 0"2(4), base plus line duad Orthogona1 (5) Icosahedral base base point isotropic point pentad axis non-isotropic point °2 (5), L1(25) minus point triad axis @ @ @ @ @ 4 3 5 5 A A A A A A A A 2A 3A 5A B* fus ind + @ @ 623 A A AB A A AB 2B 4A 6A ++ 3 -1 o -b5 ° x, + 3 -1 x. + 4 x, + 5 ind 1 2 ° -1 4 3 6 2 x, 2 ° -1 ° -1 x.

9 -1 -1 ++ 3 3 + 10 -2 000 ++ 2 -2 ind 1 2 4 3 6 Xs 4 0 -2 X. 4 0 XlO 8 0 Xl1 8 0 10 0 r2 0 0 10 0 -r2 0 0 1 2 3 3 6 6 X13 ind @ 24 24 4 3 A A A AB A A A AB 2B 2C 4B 6A X, - @ @ @ 3 BC BC 6B rus ind 0 4 5 5 A BD AD A AD BD 2D 8A 3-1 0 -1 o -1 -1 0 0 0 0 0 0-1 0 ++ 2 0 0 b5 * + 0 0 0 ++ 2 0 0 * b5 ++ -1 -1 -1 ++ 0 r2 -r2 -1 -1 ++ 0 0 00 0 i2 -i2 20 rus ind 20 4 16 16 10 rus ind 4 12 12 8 24 24 8 24 24 02 0 0 0 + 002 0 + 002 + 002 20 20 0 -1 -1 o 0 0 0 r3 o 0 0 0 0 -2 0 -1 -1 0 0 0 i3 0 -1 -1 0 -b5 * o 0 0 0 0 o 0 0 y20 *3 -1 -1 0 o 0 0 o y16 *5 0 0 o *13 y16 0 0 8 10 3-1 o 0 XIS 02 3-1 o 0 X,.

X27 02 24 0 0 0 0 -1 o .. 5AB) icosahedral 60 57 A5 1a+ 18cd+20a N(2A,3A,5AB) icosahedral 20 171 D20 la+9ab+18ccdd+20abcd N(2A). N(5AB) °2(19), L1(361) minus point 18 190 D18 1a+9 ab+ 18ccdd+ 19a+20abcd N(3A), C(2B) 02(19). base plus point Order Index 171 @ @ @ 3420 20 9 p power A A pt part ind lA A A 2A 3A @ @ @ @ @ 10 10 9 9 9 A A A A A A A A A A 5A B* 9A B*2 C*4 @ 10 BA AA lOA @ @ @ @ 10 19 19 AA A A BA A A B* 19A B** fus ind 18 A A 2B @ @ @ o 9 o -1 -1 000 o 9 o -1 -1 o 0 0 * 0 0 0 -b5 * -b5 0 0 0 * 0 0 0 b5 * -b5 0 0 0 b19 ** @ @ @ ** b19 * -1 * -b5 + 0 0 0 0 0 0 0 0 0 0 -1 ++ 0 2 0 0 0 0 b5 * b5 * -1 -1 ++ 0 2 0 0 0 0 * -1 -1 ++ 0 0 0 0 0 0 y20 *3 *9 *7 * b5 -1 -1 ++ 0 0 0 0 0 0 *7 y20 *3 *9 0 ++ -1 -1 -1 -2 0 -b5 + 18 -2 0 + 18 2 0 -b5 + 18 2 0 x.

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