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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 202 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,117)(74,97,98,113)(78,100,95,109)(82,102,103,105)(86,106,107,101)(90,110,111,99)(92,114,115,96)(104,122,123,129)(108,126,127,125)(112,130,131,121)(116,133,134,120)(118,124,136,119)(128,141,142,144)(132,145,146,140)(135,148,149,139)(137,143,151,138)(147,156,157,155)(150,159,160,154)(152,158,162,153)(161,166,167,165)(163,168,169,164)(170,172,173,171)(174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202);(1,2,5,10,19,32,49,70,95,77,56,39,26,15,24,37,54,75,99,120,138,142,127,107,85,64,45,62,83,105,125,140,154,164,167,160,149,134,115,91,113,93,118,137,152,163,170,172,166,156,141,122,100,72,47,67,90,112,132,147,158,148,130,106,80,55,34,17,29,44,61,82,104,124,114,88,63,42,25,12,3,7,14,23,36,53,74,98,73,52,35,22,13,6,11,20,33,50,71,96,119,123,103,81,60,43,28,41,58,79,101,121,139,153,157,146,131,111,89,66,87,109,129,144,155,165,171,173,169,162,151,136,117,97,68,92,116,135,150,161,168,159,145,126,102,76,51,30,46,65,86,108,128,143,133,110,84,59,38,21,8,16,27,40,57,78,94,69,48,31,18,9,4)
Conjugacy classes & character table
1363 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20068, 6);
Finite Group Databasebeta