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Aliases
Splittings
Subgroups
60 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 142 points:
(2,6,7,25,30,3,4,12,14,54)(5,19,20,79,83,9,10,41,43,122)(8,35,36,37,61,16,17,69,71,73)(11,48,49,13,53,22,23,93,27,28)(15,65,66,62,63,32,33,67,31,72)(18,75,76,59,60,38,39,117,29,107)(21,87,88,90,91,45,46,100,47,126)(24,98,99,109,116,51,52,97,74,110)(26,103,104,55,68,56,57,127,34,102)(40,106,94,115,101,58,78,82,123,128)(42,64,124,44,121,80,81,108,84,85)(50,120,112,113,125,95,96,70,130,89)(77,131,129,114,111,119,118,105,92,86)(133,135)(134,138)(136,137)(139,140);(1,2,5,11,24,53,101,129,103,79,123,63,69,111,84,41,66,65,109,71,35,70,114,90,45,19,42,82,23,50,97,127,131,39,77,120,68,110,46,89,126,73,54,49,85,106,76,83,60,88,98,59,27,4,8,18,40,56,7,15,34,14,31,64,108,113,130,124,81,62,25,55,32,12,26,58,38,16,6,13,29,52,100,107,122,117,78,121,93,30,61,91,125,87,116,102,96,119,75,118,104,99,95,48,94,80,10,21,47,92,112,17,37,74,33,67,20,44,86,36,72,115,43,57,105,128,28,51,22,9,3)(132,140,135,138,137,136,134,133,139)(141,142)
Conjugacy classes & character table
294 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23580, 17);
Finite Group Databasebeta