Finite Group Databasebeta

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C₃₁×#3178 #16843111

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

350 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)(42,48)(43,51)(45,52)(47,53)(49,54)(50,55);(33,36)(37,39)(40,41)(42,49)(43,47)(44,46)(45,50)(48,54)(51,53)(52,55);(40,42,43,48,44,50,51,55)(41,45,47,52,46,49,53,54);(32,34,35,38)(33,37,36,39)(41,46)(45,49)(47,53)(52,54)

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, 1910);