Finite Group Databasebeta

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C₃₁×#3385 #16843318

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

340 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)(32,33,36,35)(34,38,39,37)(40,41,44,48)(42,45,49,53)(43,46,51,47)(50,54,55,52);(32,34,36,39)(33,37,35,38)(40,42)(41,45)(43,50)(44,49)(46,54)(47,52)(48,53)(51,55);(41,46)(42,49)(43,51)(45,52)(47,48)(53,54);(32,35,36,33)(34,37,39,38)

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, 2117);