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C₃₁×#3136 #16843069

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

404 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)(34,37)(35,36)(38,39)(41,45)(42,48)(43,50)(46,53)(47,52)(49,54);(33,36)(37,39)(40,41,43,45,44,47,50,52)(42,46,48,51,49,53,54,55);(32,34,35,38)(33,37,36,39)(40,42,43,48,44,49,50,54)(41,46,45,51,47,53,52,55);(41,47)(45,52)(46,53)(51,55)

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, 1868);