This group can be built from two out of three of the Fischer group Fi24, the Conway group Co1, and its own    Baby  version.
Tarski names a type of group also described by the same term as this group which is an in nite group G such that any proper subgroup of the group is a cyclic group with order a  xed prime number. Prime numbers which divide the order of this group are called supersingular; there are 15 such primes. A certain collection of groups is divided into  pariahs  which are not subgroups of this one, and the  happy family  which is. This group can be built from two out of three of the Fischer group Fi24, the Conway group Co1, and its own    Baby  version. This group was initially constructed as the automorphism group of       a 196,884-dimensional algebra. For ten points, identify this largest of the 26 sporadic  nite simple groups.
Tarski names a type of group also described by the same term as this group which is an in nite group G such that any proper subgroup of the group is a cyclic group with order a  xed prime number.
Monster group