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