Finite Group Databasebeta

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C₃₁×#3117 #16843050

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

386 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)(42,48)(43,45)(44,52)(46,50)(47,51)(49,55)(53,54);(33,36)(37,39)(41,45)(46,54)(47,52)(48,55);(40,42,43,49)(41,46,45,54)(44,53,51,50)(47,55,52,48);(32,34,35,38)(33,37,36,39)(42,49)(46,54)(48,55)(50,53)

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, 1849);