Finite Group Databasebeta

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C₅₉×#444 #16836978

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

104 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)(60,61,64,68,65,62,69,67)(63,70,71,74,72,66,73,75);(60,62)(61,65)(63,70)(64,67)(66,72)(68,69)(71,74)(73,75);(60,63,64,71,65,72,69,73)(61,66,68,75,62,70,67,74)

Conjugacy classes & character table

1298 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 125);