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Aliases
Splittings
Subgroups
88 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 151 points:
(4,5)(7,8,9)(10,12,11)(14,15,17)(16,19,24)(18,22,21)(20,26,34)(23,29,31)(25,32,28)(27,36,47)(30,39,44)(33,42,41)(35,45,38)(37,49,63)(40,52,60)(43,55,57)(46,58,54)(48,61,51)(50,65,82)(53,68,79)(56,71,76)(59,74,73)(62,77,70)(64,80,67)(66,84,103)(69,87,100)(72,90,98)(75,93,95)(78,96,92)(81,85,89)(83,101,86)(88,106,121)(91,109,119)(94,112,117)(97,115,114)(99,107,111)(102,120,108)(104,122,105)(110,125,135)(113,127,134)(116,130,132)(118,126,129)(123,136,124)(128,137,144)(131,139,143)(133,138,141)(140,145,149)(142,146,148)(147,150,151);(1,2)(3,4,5)(6,7,8,10,9,11,12)(13,14,16,20,27,37,50,66,85,61,34,44,57,73,92,111,84,104,123,122,82,100,119,134,143,148,137,109,68,36,48,62,78,97,116,131,140,146,130,93,55,29,15,18,23,30,40,53,69,88,107,77,45,24,31,41,54,70,89,108,124,136,101,63,79,98,117,132,141,125,87,49,64,81,99,118,133,142,147,150,139,112,71,39,19,25,33,43,56,72,91,110,126,96,58,32,17,21,28,38,51,67,86,105,120,80,47,60,76,95,114,129,106,65,83,102,103,121,135,144,149,151,145,127,90,52,26,35,46,59,75,94,113,128,138,115,74,42,22)
Conjugacy classes & character table
1962 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35028, 178);
Finite Group Databasebeta