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Aliases
Splittings
Subgroups
60 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 126 points:
(1,4,3,2,5)(6,106,32,126,108)(7,118,95,94,51)(8,72,109,83,68)(9,78,53,100,65)(10,34,98,66,84)(11,92,114,16,112)(12,103,107,37,104)(13,89,55,122,80)(14,96,85,110,30)(15,38,82,58,101)(17,125,70,99,79)(18,54,119,31,87)(19,121,73,36,76)(20,115,61,59,24)(21,105,26,67,91)(22,46,71,102,39)(23,48,28,75,93)(25,86,88,40,90)(27,124,52,117,81)(29,64,41,123,50)(33,120,35,60,44)(42,57,97,69,62)(43,116,47,74,49)(45,63,113,56,111);(1,2,4,3,5)(6,44,88,71,11,27,82,65,75,25,117,48,93,122,13,87,24,55,98,7,54,108,41,115,111,92,80,123,103,84,60,12,95,72,57,31,70,85,106,86,66,50,99,76,59,36,26,63,46,35,16,53,124,89,61,94,29,112,104,37,62,14,34,73,21,33,81,118,107,110,67,51,105,77,83,38,8,69,47,58,18,45,109,79,100,42,30,74,49,126,22,15,40,28,119,10,32,113,64,120,68,17,90,125,121,39,9,20,114,97,19,52,96,91,101,43,56,78,116,102,23)
Conjugacy classes & character table
145 conjugacy classes — view the full character table.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 970);
Finite Group Databasebeta