Finite Group Databasebeta

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C₃₁×#2782 #16842715

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(33,36)(34,38)(40,41,43,45)(42,46,47,44)(48,49)(50,53)(51,52)(54,55);(33,36)(37,39)(49,51)(50,54);(32,33)(34,37)(35,36)(38,39)(40,41)(42,44)(43,45)(46,47)(48,50,52,54)(49,53,51,55);(32,34,35,38)(33,37,36,39)(40,42,43,47)(41,44,45,46)(48,51,52,49)(50,55,54,53)

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, 1514);