####################################################################################
###
### Python code accompanying the paper
###    'The maximal subgroups of the Monster'
### by Dietrich, Lee, Popiel (2023)
###
###  * Generators for the maximal PGL(2,13)
###
####################################################################################

from mmgroup import *

### Generators of L = PGL(2,13) = <g13, g6, i2, a12>,
### where g13, g6, i2, a12 have orders 13, 6, 2, 12.
###
### We have PSL(2,13) = <g13, g6, i2> with <g13,g6> = 13:6 and <g6,i2> = D12
###

g13 = MM("M<y_519h*x_0cb8h*d_3abh*p_178084032*l_2*p_2344320*l_2*p_471482*l_1*t_1*l_2*p_2830080*l_2*p_22371347*l_2*t_2*l_1*p_1499520*l_2*p_22779365*l_2*t_1*l_2*p_2597760*l_1*p_11179396*t_1*l_1*p_1499520*l_2*p_85838017*t_2*l_1*p_1499520*l_1*p_64024721*t_2*l_2*p_2386560*l_2*p_21335269>")

g6 = MM("M<y_764h*x_590h*d_0bf6h*p_63465756*l_1*p_24000*l_2*p_528432*t_1*l_2*p_1457280*l_1*p_23214136*l_1*t_2*l_2*p_2344320*l_2*p_13038217*l_2*t_1*l_2*p_2956800*l_1*p_85332887*t_2*l_2*p_2830080*l_2*p_85335745*t_2*l_2*p_1900800*l_2*p_13472*t_2*l_2*p_2386560*l_2*p_85413728*t_1*l_2*p_2386560*l_2*p_53803593>")

i2 = MM("M<y_6ch*x_7ch*d_52ah*p_115885662*l_2*p_2787840*l_2*p_12552610*l_2*t_1*l_2*p_1900800*l_2*p_31998118*l_2*t_2*l_2*p_80762880*l_1*p_243091248*l_2*t_1*l_2*p_2597760*l_1*p_42794439*t_1*l_1*p_1394880*l_2*p_64015152*t_1*l_1*p_2027520*l_1*p_177984*t_1*l_2*p_79432320*l_1*p_161927136>")

a12 = MM("M<y_1afh*x_1661h*d_2ddh*p_208095583*l_2*p_1943040*l_2*p_1974295*l_2*t_2*l_2*p_1900800*l_2*p_10778*l_2*t_2*l_2*p_1900800*l_2*p_1868387*l_1*t_1*l_2*p_2956800*l_1*p_11159238*t_1*l_2*p_1985280*l_1*p_86275805*t_2*l_2*p_2386560*l_2*p_42712609*t_2*l_1*p_1499520*l_1*p_106699812>")


### Standard generators of order 12 and 4 as in Magma. Gerald Hoehn.

a = MM("M<y_3c4h*x_174h*d_3aah*p_88936484*l_1*p_1499520*l_1*p_21440981*t_1*l_2*p_1943040*l_2*p_466918*l_2*t_1*l_2*p_2597760*l_1*p_32114353*l_1*t_1*l_2*p_1985280*l_1*p_22752488*t_1*l_2*p_1393920*l_2*p_23376*l_1*p_1968960*t_2*l_1*p_2999040*l_1*p_932280>")

b = MM("M<y_0ch*x_908h*d_39bh*p_138589461*l_2*p_2830080*l_2*p_12106115*l_2*t_2*l_1*p_1499520*l_1*p_22276076*l_1*t_2*l_2*p_2830080*l_2*p_2413937*l_2*t_1*l_2*p_1943040*l_2*p_42677968*t_1*l_1*p_1499520*l_2*p_64082407*t_2*l_2*p_2386560*l_2*p_127992596*t_2*l_2*p_1985280*l_1*p_53904594*t_1*l_2*p_2597760*l_1*p_64047779>")