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C₃₁×#3011 #16842944

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

700 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 67 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)(34,35)(36,37,41,45)(38,46,49,59)(39,43,50,57)(40,52,54,44)(42,53,56,48)(47,60,61,67)(51,64,63,58)(55,65,66,62);(36,38,41,49)(37,42,45,56)(39,47,50,61)(40,53,54,48)(43,55,57,66)(44,59,52,46)(51,65,63,62)(58,67,64,60);(33,35)(36,39)(37,43)(38,47)(40,51)(41,50)(42,55)(44,58)(45,57)(46,60)(48,62)(49,61)(52,64)(53,65)(54,63)(56,66)(59,67);(39,50)(43,57)(47,61)(51,63)(55,66)(58,64)(60,67)(62,65)

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, 1743);