Lyons group The
Lyons group, Ly, is the unique group (up to
isomorphism) that has in
involution t where C_G(t) is the
covering group of the
alternating group A_{11}, and t is not
weakly closed in C_G(t).
Richard Lyons, the namesake of these groups, was the first to consider their properties, including their
order, and
Charles Sims proved with machine calculation that such a group must exist and be unique. The group has an order of 2^8 \cdot 3^7 \cdot 5^6 \cdot 7 \cdot 11 \cdot 31 \cdot 37 \cdot 67.
O'Nan group Rudvalis group The
Rudvalis group is a finite simple group R that is a rank 3
permutation group on 4060 letters where the
stabilizer of a point is the
Ree group. The group was described by
Arunas Rudvalis, who proved the existence of such a group. This group has order of 145,926,144,000=2^{14} \cdot 3^3 \cdot 5^3 \cdot 7 \cdot 13 \cdot 29.
Janko groups J4 J3 J1 ==References==