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Aliases
Subgroups
110 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 86 points:
(1,2,3,4,5)(6,7,11,9,13,23,19,29,44,10,14,24,20,30,45,38,53,67,21,31,46,39,54,68,60,74,82)(8,12,22,17,27,42,36,51,65,18,28,43,37,52,66,59,73,81,16,26,41,35,50,64,58,72,80)(15,25,40,33,48,62,56,70,78,32,47,61,55,69,77,75,83,85,34,49,63,57,71,79,76,84,86);(6,8,15)(7,12,25)(9,17,33)(10,18,32)(11,22,40)(13,27,48)(14,28,47)(16,34,21)(19,36,56)(20,37,55)(23,42,62)(24,43,61)(26,49,31)(29,51,70)(30,52,69)(35,57,39)(38,59,75)(41,63,46)(44,65,78)(45,66,77)(50,71,54)(53,73,83)(58,76,60)(64,79,68)(67,81,85)(72,84,74)(80,86,82);(8,16,18)(12,26,28)(15,32,34)(17,35,37)(22,41,43)(25,47,49)(27,50,52)(33,55,57)(36,58,59)(40,61,63)(42,64,66)(48,69,71)(51,72,73)(56,75,76)(62,77,79)(65,80,81)(70,83,84)(78,85,86)
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(1215, 50);
Finite Group Databasebeta