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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 144 points:
(4,8,9,7,12,5,6,13,10,11)(15,19,20,38,43,16,17,25,27,64)(18,32,33,88,82,22,23,54,56,119)(21,48,49,50,69,29,30,78,80,42)(24,39,60,102,65,35,36,66,63,105)(26,34,68,95,116,40,41,58,109,104)(28,73,74,70,71,45,46,75,44,81)(31,83,53,89,120,51,52,85,86,125)(37,79,101,96,131,61,62,117,132,133)(47,107,108,127,121,76,67,136,92,124)(55,84,103,126,77,90,91,99,106,115)(57,128,129,111,112,93,94,142,72,138)(59,134,135,144,143,97,98,130,139,118)(87,110,140,141,137,122,123,113,114,100);(1,2)(3,4,7,12,6,9,13,8,11,10,5)(14,15,18,24,37,63,103,97,41,32,55,49,81,118,125,119,80,48,79,46,75,114,135,128,93,54,89,126,60,100,133,109,139,108,134,123,58,96,129,140,111,70,38,65,52,84,121,56,92,112,117,107,36,20,28,47,77,116,43,69,40,17,21,31,53,87,122,85,51,29,19,26,42,64,104,115,76,45,25,39,67,101,138,127,88,124,91,83,105,27,44,72,113,142,132,68,110,98,136,144,95,131,137,66,106,86,33,57,94,130,141,74,73,62,30,50,82,120,143,71,78,90,23,34,59,99,102,61,35,22,16)
Conjugacy classes & character table
308 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28820, 43);
Finite Group Databasebeta