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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 146 points:
(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(17,21,22,40,45,18,19,27,29,69)(20,34,35,94,98,24,25,56,58,137)(23,50,51,52,76,31,32,84,86,88)(26,63,64,28,68,37,38,108,42,43)(30,80,81,77,78,47,48,82,46,87)(33,90,91,74,75,53,54,132,44,122)(36,102,103,105,106,60,61,115,62,141)(39,113,114,124,131,66,67,112,89,125)(41,118,119,70,83,71,72,142,49,117)(55,121,109,130,116,73,93,97,138,143)(57,79,139,59,136,95,96,123,99,100)(65,135,127,128,140,110,111,85,145,104)(92,146,144,129,126,134,133,120,107,101);(1,2)(3,4,6,8,10,12,14,15,13,11,9,7,5)(16,17,20,26,39,68,116,144,118,94,138,78,84,126,99,56,81,80,124,86,50,85,129,105,60,34,57,97,38,65,112,142,146,54,92,135,83,125,61,104,141,88,69,64,100,121,91,98,75,103,113,74,42,19,23,33,55,71,22,30,49,29,46,79,123,128,145,139,96,77,40,70,47,27,41,73,53,31,21,28,44,67,115,122,137,132,93,136,108,45,76,106,140,102,131,117,111,134,90,133,119,114,110,63,109,95,25,36,62,107,127,32,52,89,48,82,35,59,101,51,87,130,58,72,120,143,43,66,37,24,18)
Conjugacy classes & character table
418 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34060, 33);
Finite Group Databasebeta