Finite Group Databasebeta

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C₃₁×#2966 #16842899

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

380 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)(40,41,43,47,44,46,50,53)(42,45,48,52,49,51,54,55);(33,36)(37,39);(40,42,43,48,44,49,50,54)(41,45,47,52,46,51,53,55);(32,34,35,38)(33,37,36,39)(41,46)(45,51)(47,53)(52,55)

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1698);