Finite Group Databasebeta

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C₅₉×#455 #16836989

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

152 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)(60,61,64,67)(62,68,70,75)(63,71,73,66)(65,72,74,69);(60,62)(61,65)(63,72)(64,70)(66,75)(67,74)(68,71)(69,73);(63,73)(66,71)(68,75)(69,72)

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, 136);