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C₅₉×#585 #16837119

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 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)(62,68)(63,67)(64,66)(65,69)(70,74)(71,73)(72,75);(60,62)(61,65)(63,70)(64,69)(66,68)(67,72)(71,75)(73,74);(62,69)(65,68)(70,75)(72,74);(61,66)(65,68)(67,73)(72,74);(60,63,64,71)(61,67,66,73)(62,70,69,75)(65,72,68,74)

Conjugacy classes & character table

2006 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 266);