Finite Group Databasebeta

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C₃₁×#1837 #16841770

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 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)(40,41,44,50,46,51,45,49)(42,48,43,47,53,54,52,55);(33,36)(37,39)(40,42,45,52,46,53,44,43)(41,47,50,54,51,55,49,48);(32,34,35,38)(33,37,36,39)(40,43,44,53,46,52,45,42)(41,48,49,55,51,54,50,47)

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 569);