THE 5-MODULAR CHARACTERS OF THE SPORADIC SIMPLE FISCHER GROUP-FI22 AND GROUP-FI23

The 5-modular decomposition numbers of the two simple Fischer groups F i22 and Fi23, and also those of the two maximal subgroups 2. Fi22 and O8+(3).S3 of Fi23 are determined. In AIL appendix Thomas Breuer commen ts on his construction of the ordinary character tables of the groups 2(2). U6(2) and O8+(3).S3, which occur as maximal subgroups of 2.Fi22 respectively Fi23. The results were obtained with the help of the comp uter algebra systems MOC [4] and GAP [10].