Finite Group Databasebeta

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C₅₉×#456 #16836990

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 75 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)(60,61,65,63)(62,68,71,75)(64,72,74,67)(66,73,69,70);(60,62)(61,66)(63,69)(64,73)(65,71)(67,75)(68,72)(70,74);(60,63,65,61)(62,69,71,66)(64,67,74,72)(68,73,75,70)

Conjugacy classes & character table

944 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 137);