Order = 562000363888803840000 = 18.104.22.168.22.214.171.124.
Mult = 2.
Out = 2.
Standard generators of A22 are a, b where a is in class 3A, b has order 21 (necessarily a 21-cycle), ab has order 20 and [a,b] has order 2.
Standard generators of S22 are c, d where c is in the smallest conjugacy class of outer involutions, d has order 21 (necessarily a 21-cycle) and cd has order 22.
Checking generators (semi-presentations)
|A22||〈〈 a, b | some conditions 〉〉||Download|
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 22 Std Details 231 Std Details
- Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 21 Std Details 0 Z 209 Std Details 0 Z 210 Std Details