Finite Group Databasebeta

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C₃₁×#3113 #16843046

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

380 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)(34,37)(35,36)(38,39)(40,41,44,47)(42,48,49,55)(43,51,53,46)(45,52,54,50);(33,36)(37,39);(40,42,44,49)(41,45,47,54)(43,52,53,50)(46,55,51,48);(32,34,35,38)(33,37,36,39)(42,49)(45,54)(48,55)(50,52)

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, 1845);