Finite Group Databasebeta

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C₃₁×#2969 #16842902

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

370 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)(40,41,43,46,44,47,50,53)(42,45,49,52,48,51,54,55);(33,36)(37,39)(42,48)(45,51)(49,54)(52,55);(40,42,43,49,44,48,50,54)(41,45,46,52,47,51,53,55);(32,34,35,38)(33,37,36,39)(42,48)(45,51)(49,54)(52,55)

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1701);