Finite Group Databasebeta

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C₃₁×#1838 #16841771

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 55 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)(34,37)(35,36)(38,39)(40,41,45,49,46,50,44,54)(42,51,52,55,53,48,43,47);(33,36)(37,39)(40,42,44,43,46,53,45,52)(41,47,49,51,50,55,54,48);(32,34,35,38)(33,37,36,39)(40,43,44,53,46,52,45,42)(41,48,49,47,50,51,54,55)

Conjugacy classes & character table

992 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 570);