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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 220 points:
(2,3,5,9,17,33,62)(4,7,13,25,44,80,133)(6,11,21,41,75,126,108)(8,15,29,54,96,47,24)(10,19,37,14,27,50,90)(12,23,45,82,136,185,182)(16,31,58,100,154,196,116)(18,35,64,110,34,55,97)(20,39,71,72,120,134,183)(22,43,78,113,159,175,147)(26,49,88,143,103,91,148)(28,52,93,151,68,30,56)(32,60,104,135,118,109,87)(36,66,112,95,81,67,114)(38,69,46,84,127,61,106)(40,73,122,144,142,86,53)(42,77,129,179,51,92,149)(48,85,140,180,63,98,57)(59,102,121,169,189,202,115)(65,101,156,76,128,177,165)(70,117,94,153,186,131,166)(74,124,107,162,79,132,168)(83,138,173,190,158,150,195)(89,145,193,204,176,141,99)(105,160,192,194,184,170,167)(111,157,172,137,187,209,206)(119,123,171,191,161,152,197)(125,155,198,208,181,164,146)(130,163,201,139,178,174,200)(188,199,210,211,205,207,203)(212,213,215,214,216,218,217,219,220);(1,2,4,8,16,32,61,107,163,202,54,60,105,161,82,137,43,79,90,147,69,116,96,112,73,123,172,203,114,166,102,157,193,187,185,13,26,49,89,146,194,77,130,23,46,85,126,175,129,180,206,31,59,103,158,171,21,42,62,108,37,68,115,167,39,72,121,170,66,113,58,101,153,136,186,208,183,25,48,87,142,41,76,11,22,44,81,135,184,207,210,15,30,57,99,122,128,178,205,140,189,195,201,169,19,38,70,118,35,65,111,64,93,152,156,200,133,182,56,98,143,191,197,5,10,20,40,74,125,174,198,7,14,28,53,95,75,127,176,84,139,149,162,120,9,18,36,67,17,34,63,109,164,160,100,155,199,209,29,55,92,150,151,196,132,181,52,94,145,177,154,3,6,12,24,47,86,141,190,45,83,97,106,71,119,138,188,80,134,148,179,117,168,104,159,124,173,204,211,33,50,91,110,165,78,131,27,51,88,144,192)
Conjugacy classes & character table
333 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13293, 3);
Finite Group Databasebeta