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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 108 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108);(8,10,9,11)(13,108)(14,107)(15,106)(16,105)(17,104)(18,103)(19,102)(20,101)(21,100)(22,99)(23,98)(24,97)(25,96)(26,95)(27,94)(28,93)(29,92)(30,91)(31,90)(32,89)(33,88)(34,87)(35,86)(36,85)(37,84)(38,83)(39,82)(40,81)(41,80)(42,79)(43,78)(44,77)(45,76)(46,75)(47,74)(48,73)(49,72)(50,71)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61)
Conjugacy classes & character table
700 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2716, 3);
Finite Group Databasebeta