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C₃₁×#2017 #16841950

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 63 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)(34,43)(35,48)(36,53)(37,41)(38,42)(39,45)(40,51)(44,61)(46,56)(47,55)(49,60)(50,59)(52,58)(54,62)(57,63);(32,34)(33,39)(35,49)(36,46)(37,45)(38,47)(40,57)(41,55)(42,56)(43,53)(44,50)(48,54)(51,62)(52,63)(58,61)(59,60);(32,35)(33,40)(34,44)(36,50)(37,51)(38,52)(39,54)(41,58)(42,59)(43,60)(45,49)(46,63)(47,62)(48,53)(55,57)(56,61)

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, 749);