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C₃₁×#3177 #16843110

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 71 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)(40,41,45,49)(42,46,51,59)(43,53,56,68)(44,57,54,48)(47,61,62,55)(50,63,65,71)(52,67,64,60)(58,69,70,66);(33,36)(37,39)(40,42,45,51)(41,46,49,59)(43,50,56,65)(44,52,54,64)(47,58,62,70)(48,60,57,67)(53,63,68,71)(55,66,61,69);(40,43,54,61,45,56,44,55)(41,47,57,68,49,62,48,53)(42,50,64,69,51,65,52,66)(46,58,67,71,59,70,60,63);(32,34,35,38)(33,37,36,39)(42,51)(46,59)(50,65)(52,64)(58,70)(60,67)(63,71)(66,69)

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, 1909);