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C₅×#6873 #11925946

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 86 points:

(1,2,3,4,5)(6,7,11,9,14,26,21,32,48,23,13,29,44,31,53,67,56,74,10,15,25,22,33,47,43,57,70)(8,16,34,19,36,59,41,61,78,18,12,24,40,28,46,65,51,69,20,30,52,42,55,73,66,76,84)(17,35,45,38,60,68,63,79,82,39,27,49,64,50,71,81,72,83,37,54,58,62,75,77,80,85,86);(6,8,17)(7,12,27)(9,19,38)(10,20,37)(11,24,45)(13,30,54)(14,28,50)(15,16,35)(18,39,23)(21,41,63)(22,42,62)(25,34,58)(26,46,68)(29,52,49)(31,55,75)(32,51,72)(33,36,60)(40,64,44)(43,66,80)(47,59,77)(48,69,82)(53,73,71)(56,76,85)(57,61,79)(65,81,67)(70,78,86)(74,84,83)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 20);