Numbers in group theory

This page contains numbers appearing in.

List of numbers in group theory

 * The has 101 es.
 * The largest of any element in the Monster group is 119. There is also no other  with elements of larger order.
 * The  has  133.
 * The McKay-Thompson series of span a 163-.
 * 168 is the order of the, which is isomorphic to GL(3,2).
 * The exceptional Lie algebra has dimension 190.
 * There are 194 es in the Monster group.
 * The exceptional Lie algebra has dimension 248.
 * 360 is the of the alternating group of degree 6, which is isomorphic to the matrix group, and to . It is one of the few non-abelian simple groups with only three distinct prime factors in the order.
 * 1,092 is the order of the simple group.
 * 2,448 is the order of the matrix group . It is one of the few non-abelian simple groups with only three distinct prime factors in the order.
 * There are 4,060 points in the smallest faithful permutation representation of the ; its one-point stabilizer is the automorphism group of the.
 * 4,080 is the order of the simple group, which is isomorphic to PGL(2,16) and SL(2,16). It is one of the few over a finite field of characteristic 2, for which the Sylow 2-subgroup is not the largest.
 * The smallest faithful linear representation of the Baby monster group over any field has dimension 4,370.
 * The smallest faithful linear representation of the Baby monster group over the complex numbers has dimension 4,371.
 * The coefficient of the linear term in the T2A is equal to 4,372.
 * 5,616 is the order of the matrix group, which is isomorphic to PGL(3,3) and SL(3,3). It is one of the few non-abelian simple groups with only three distinct prime factors in the order.
 * 6,048 is the order of the simple group, which is isomorphic to . It is one of the few non-abelian simple groups with only three distinct prime factors in the order.
 * 20,160 is the smallest order with more than one simple group.
 * One of them is the alternating group of degree 8, which is isomorphic to the matrix groups, PGL(4,2), PSL(4,2), and SL(4,2).
 * The other is the Mathieu group of degree 21, which is isomorphic to the matrix group PSL(3,4).
 * 25,920 is the order of the simple group, which is isomorphic to . It is one of the few non-abelian simple groups with only three distinct prime factors in the order.
 * 181,440 is the order of the of degree 9. It is the largest alternating group, for which the Sylow 2-subgroup is not the largest Sylow subgroup.
 * The smallest faithful linear representation of the Monster group over any field has dimension 196,882.
 * The smallest faithful linear representation of the Monster group over the complex numbers has dimension 196,883.
 * The has dimension 196,884.
 * It is also the coefficient of the linear term in the of the.
 * There are (5)=9,999,360 5 × 5  over, therefore it is the order of a matrix group.
 * 16,776,960 is the order of the simple group, which is isomorphic to PGL(2,256) and SL(2,256). It is one of the few over a finite field of characteristic 2, for which the Sylow 2-subgroup is not the largest Sylow subgroup.
 * The order of a simple group is almost never a . The emphasis is on "almost", since for s, the order of the simple group is a square number. The simple group  has order 138,297,600, which is the smallest perfect power that is also an order of a simple group.
 * The order of a simple group is almost never an . The emphasis is on "almost", since there is a simple group of order 16,938,986,400, which is an Achilles number.
 * 281,474,976,645,120 is the order of the simple group, which is isomorphic to PGL(2,65536) and SL(2,65536). It is one of the few over a finite field of characteristic 2, for which the Sylow 2-subgroup is not the largest Sylow subgroup.