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C₃₁×#2824 #16842757

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

472 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)(33,36)(37,39)(40,41,43,44)(42,45,47,46)(48,49)(50,53)(51,52)(54,55);(34,38)(37,39)(41,44)(45,46)(49,52)(53,54);(32,33)(34,37)(35,36)(38,39)(40,41)(42,46)(43,44)(45,47)(48,50)(49,53)(51,55)(52,54);(32,34)(33,37)(35,38)(36,39)(40,42)(41,45)(43,47)(44,46)(48,49)(50,54)(51,52)(53,55)

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, 1556);