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C₃₁×#2845 #16842778

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

Conjugacy classes & character table

806 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1577);