Finite Group Databasebeta

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C₃₁×#3326 #16843259

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

392 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)(42,48)(43,51)(44,46)(45,50)(47,53)(49,55)(52,54);(32,34)(33,36)(35,39)(37,38)(42,49)(45,54)(48,55)(50,52);(40,42,44,49)(41,45,46,54)(43,52,53,50)(47,55,51,48);(34,39)(36,38)(41,46)(45,54)(47,51)(48,55)

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, 2058);