Order = 60822550204416000 = 22.214.171.124.126.96.36.199.
Mult = 2.
Out = 2.
Standard generators of A19 are a, b where a is in class 3A, b has order 17 and ab has order 19.
Standard generators of S19 are c, d where c is in the smallest conjugacy class of outer involutions, d has order 18 (necessarily an 18-cycle) and cd has order 19.
Checking generators (semi-presentations)
|A19||〈〈 a, b | some conditions 〉〉||Download|
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 19 Std Details 171 Std Details 969 Std Details
- Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 18 Std Details 0 Z 152 Std Details 0 Z 153 Std Details