Finite Group Databasebeta

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C₃₁×#3316 #16843249

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

388 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)(32,33,35,37)(34,38,39,36)(40,41,44,47)(42,48,49,55)(43,51,53,46)(45,52,54,50);(32,34)(33,36)(35,39)(37,38)(42,49)(45,54)(48,55)(50,52);(40,42,44,49)(41,45,47,54)(43,52,53,50)(46,55,51,48);(34,39)(36,38)

Conjugacy classes & character table

899 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2048);