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Aliases
Splittings
Subgroups
120 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 199 points:
(4,5)(7,8)(10,14,15,33,38,11,12,20,22,61)(13,27,28,93,98,17,18,49,51,136)(16,43,44,45,72,24,25,81,83,85)(19,56,57,146,124,30,31,107,109,180)(21,66,67,129,130,35,36,122,71,112)(23,76,58,73,74,40,41,77,39,84)(26,87,88,156,135,46,47,143,145,80)(29,103,97,195,132,53,54,160,161,133)(32,75,111,52,165,59,60,110,100,101)(34,116,117,62,128,63,64,171,113,114)(37,127,82,92,104,69,70,138,139,152)(42,55,134,162,163,78,79,105,99,190)(48,150,151,187,181,90,91,179,149,199)(50,157,158,121,198,95,96,192,176,169)(65,175,164,153,102,119,120,182,144,167)(68,154,155,86,170,125,94,189,141,115)(89,186,172,173,137,147,148,118,196,106)(108,183,177,178,166,131,140,123,184,197)(126,193,185,191,168,174,159,188,194,142);(1,2)(6,7,8)(9,10,13,19,32,60,73,33,62,115,114,127,182,162,93,153,47,89,149,188,88,146,96,159,194,145,154,28,52,102,168,141,83,43,82,101,166,198,130,38,72,132,41,77,56,108,129,69,35,12,16,26,48,92,111,107,64,118,174,125,66,123,179,155,190,91,134,184,192,148,117,161,196,199,180,122,54,104,98,135,78,40,20,34,65,121,175,183,74,81,137,79,53,27,50,97,160,95,18,29,55,106,44,84,140,120,176,119,63,15,23,42,80,136,152,103,67,124,181,173,195,171,186,158,178,105,150,163,189,151,177,36,68,126,172,116,57,110,139,90,46,24,14,21,37,71,131,31,58,76,133,85,61,112,169,197,165,138,25,45,86,142,167,100,49,94,156,191,193,157,109,143,185,187,147,87,144,51,99,164,70,128,170,113,22,39,75,59,30,17,11);(3,4,5)
Conjugacy classes & character table
402 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34380, 69);
Finite Group Databasebeta