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Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 138 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,14,16)(15,18,23)(17,21,20)(19,25,33)(22,28,30)(24,31,27)(26,35,46)(29,38,43)(32,41,40)(34,44,37)(36,48,62)(39,51,59)(42,54,56)(45,57,53)(47,60,50)(49,64,80)(52,66,77)(55,69,74)(58,72,71)(61,75,68)(63,78,65)(67,83,96)(70,85,93)(73,88,90)(76,91,87)(79,94,84)(81,97,82)(86,100,110)(89,102,107)(92,105,104)(95,108,101)(98,111,99)(103,114,121)(106,116,118)(109,119,115)(112,122,113)(117,125,129)(120,127,126)(123,130,124)(128,133,134)(131,135,132)(136,138,137);(12,13,15,19,26,36,49,64,81,98,112,123,131,136,135,119,91,57,31,16,20,27,37,50,65,82,83,48,63,79,95,109,120,128,130,108,75,44,23,30,40,53,68,84,99,100,66,35,47,61,76,92,106,117,122,94,60,33,43,56,71,87,101,113,114,85,51,25,34,45,58,73,89,103,111,78,46,59,74,90,104,115,124,125,102,69,38,18,24,32,42,55,70,86,97,62,77,93,107,118,126,132,133,116,88,54,28,14,17,22,29,39,52,67,80,96,110,121,129,134,137,138,127,105,72,41,21)
Conjugacy classes & character table
495 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4191, 1);
Finite Group Databasebeta