← Prev (#45684740) Next (#45684742) →
Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 164 points:
(4,8,9,7,12,5,6,13,10,11)(15,19,20,38,43,16,17,25,27,66)(18,32,33,95,99,22,23,54,56,139)(21,48,49,50,76,29,30,85,86,88)(24,60,61,131,119,35,36,105,106,112)(26,71,65,126,59,40,41,75,110,104)(28,80,81,77,78,45,46,82,44,87)(31,90,91,142,143,51,52,134,98,158)(34,96,97,154,127,58,55,141,122,103)(37,100,109,47,129,63,64,145,83,84)(39,113,114,67,53,68,69,150,111,93)(42,123,124,151,135,73,74,138,156,161)(57,62,146,118,128,101,102,108,79,153)(70,148,147,140,160,116,117,107,163,164)(72,144,125,89,94,120,121,157,132,133)(92,162,149,152,130,136,137,115,155,159);(1,2)(3,4,7,12,6,9,13,8,11,10,5)(14,15,18,24,37,65,73,40,17,21,31,53,94,121,142,96,23,34,59,43,76,127,101,54,36,62,106,78,85,130,160,97,64,95,140,128,91,135,99,143,110,61,107,148,137,114,145,157,123,108,149,113,151,152,154,120,71,119,111,27,44,79,116,68,20,28,47,46,82,124,136,90,30,50,89,84,129,132,86,48,52,92,138,81,80,83,45,25,39,70,118,77,38,67,112,41,72,122,155,156,69,115,146,74,125,109,150,162,117,147,105,126,158,139,161,134,153,163,56,100,141,164,159,49,87,131,102,60,33,57,103,88,66,104,58,32,55,98,144,133,93,51,29,19,26,42,75,63,35,22,16)
Conjugacy classes & character table
352 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33220, 45);
Finite Group Databasebeta