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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)(15,19,20,38,43,16,17,25,27,67)(18,32,33,94,99,22,23,54,56,72)(21,48,49,50,73,29,30,83,85,87)(24,61,62,144,138,35,36,106,105,159)(26,60,70,107,150,40,41,66,119,113)(28,77,78,74,75,45,46,79,44,86)(31,89,90,141,71,51,52,101,120,42)(34,102,103,130,121,58,59,98,88,157)(37,109,110,122,100,64,65,76,147,57)(39,108,117,68,151,63,69,146,114,115)(47,124,125,53,136,80,81,158,92,93)(55,135,140,126,112,96,97,123,160,149)(82,153,95,163,164,116,127,137,139,156)(84,148,104,145,143,111,129,142,132,152)(91,162,154,155,128,133,134,118,131,161);(1,2)(3,4,7,12,6,9,13,8,11,10,5)(14,15,18,24,37,66,112,150,43,73,121,115,152,142,102,141,99,71,40,17,21,31,53,94,138,158,62,75,83,128,153,90,100,54,95,136,103,96,23,34,60,105,139,164,154,108,122,129,160,124,134,117,97,133,89,132,119,36,63,20,28,47,82,114,27,44,76,78,77,123,155,130,85,48,84,109,65,111,30,50,88,131,140,46,79,110,74,38,68,116,80,45,25,39,61,107,145,52,91,135,146,162,81,126,148,147,69,118,156,163,144,41,58,32,55,98,93,137,33,57,101,127,161,49,86,106,125,159,56,92,51,29,19,26,42,72,120,59,104,143,151,157,87,67,113,149,70,64,35,22,16)
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, 44);
Finite Group Databasebeta