By John Horton Conway

ISBN-10: 0198531990

ISBN-13: 9780198531999

This atlas covers teams from the households of the type of finite uncomplicated teams. lately up-to-date incorporating corrections

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**Additional info for Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups**

**Example text**

4 Character Abstract Linear 2 4 :<3 xO lO) 24 : 15:4 la+15a N(2A 4 ) point L2 (4) 50 5S A5 A x 2 5 (A5 x2)'2 la+15a+17abc N(2A,3A,5AB), C(2B) 34 120 0 34 17:4 17:S 1a+17abcdefg N(17A-H) 30 135 0 30 s3 x 5:4 la+15a+17abcdefg N(3A), N(5AB) Orthogonal (15) Orthogonal (4) isotropic point isotropic point 03(4) non-isotropic point °2(15), plus line @ @ 40S0 15 P power pt part A A ind 1A 2A @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ -1 ° 0 0 0 0 0 0-y17 + 15 -1 o 0 0 0 0 0 + 15 -1 o 0 ° 0 0 + 15 -1 o 0 0 0 + 15 -1 ° 0 0 + 15 -1 o 0 + 15 -1 o + 15 -1 o Xw + 15 Xu + 17 -1 2 2 -1 -1 -1 -1 + 17 2 b5 * b5 b5 * * o o + 17 2 * b5 * * b5 b5 o + 17 -1 * b5 y15 *4 *2 *S + 17 -1 * b5 *4 y15 *S + 17 -1 b5 * *S *2 y15 + 17 -1 b5 * *2 *S X16 [12] 3 @ @ @ 50 4 3 5 A A AB BB A A AB AB 2B 4A 5A lOA @ 5 AB BB B* fus ind ++ 15 Xu @ 15 15 15 15 15 15 15 17 17 17 17 17 17 17 17 A A A BA BA AA AA A A A A A A A A A A A AA AA BA BA A A A A A A A A 3A 5A B* 15A B*4 C*2 O*S 17A B*4 C*2 O*S E*5 F*7 G*5 H*3 fus ind + x, 5 pair of isotropic points + x.

2 : the automorphism group of a generalized hexagon of order (2,2) consisting of 63 vertices and 63 edges, each object being incident with 3 of the-other type. 2 : the automorphism group of the F 2 Cayley algebra, whose elements are integral Cayley numbers modulo doubles of Cayley (2) integral Cayley numbers (see below). A pair {x,y} {O,1} of elements with x+Y ~ =1 is either isotropic with x2 =y2=O (36 cases), non-isotropic with x 3 =y3: 1 (28), or mixed with x 2 =O, y2=l t or vice versa (63). 2 the automorphism group of the integral Cayley algebra in which i oo =1, i n+1 =i, i n +2 =j, i n +4 =k define a quaternion subalgebra for each n (subscripts modulo 7); ~xnin is integral provided that all 2x n are integral and the set of n for which xn is integral is one of (0124l, (0235), (0346l, (0156l, (00013l, (00026), (00045), (000123456l or their complements.

Morris J. A. Todd D. Enomoto H. N. Ward B. Srinivasan J. McKay and D. Wales D. Gabrysch D. C. Hunt J. S. Frame, A. Rudvalis, and collaborators B. Fischer, D. Livingstone, M. (2), [the Monster], and finally the Aachen 'CAS' team led by J. Neubtiser and H. Pahlings both for many original tables and for improvements, extensions, and corrections to many others. Among our group-theoretical colleagues at Cambridge who have used the A lr ILA§ and contributed tables, corrections, improvements, or criticism are David Benson, Patrick Brooke, Mike Guy, David Jackson, Gordon James, Peter Kleidman, Martin Liebeck, Nick Patterson, Larissa Queen, Alex Ryba, Jan Saxl, Peter Smith, and finally John Thompson, who has acted as our friend and mentor throughout.

### Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups by John Horton Conway

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