Finite Group Databasebeta

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C₅₉×#472 #16837006

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

108 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)(61,65)(62,69)(63,66)(68,73)(70,71)(72,74);(60,61,66,73,64,68,63,65)(62,67,69,74,71,75,70,72);(60,62)(61,67)(63,70)(64,71)(65,72)(66,69)(68,75)(73,74)

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, 153);