← Prev (#27210702) Next (#27210704) →
Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 87 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,59)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,55,54,40,49,65)(34,62,63,50,48,56)(37,42,61,51,52,57)(53,60,66,58,64,67)(69,70)(71,72)(73,74)(75,76)(77,78)(79,83,87,81,86,82,84,80,85);(1,2,5,11,19,32,36,10,16,24,38,54,66,64,31,48,55,57,59,63,28,43,44,27,42,58,51,35,22,7,6,12,21,34,50,33,20,4,8,13,23,37,53,52,18,29,39,41,56,47,61,49,62,46,60,67,65,45,15,26,14,25,40,30,17,9,3)(68,69,71,73,75,77,78,76,74,72,70)
Polycyclic presentation:
2,3,11,67,3|b^3=e,c^a=c^10,d^a=d^66,d^b=d^37
Conjugacy classes & character table
426 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13266, 17);
Finite Group Databasebeta