Finite Group Databasebeta

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C₃₁×#3377 #16843310

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

332 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)(33,36)(37,38)(40,41,45,48)(42,49,50,55)(43,47,44,52)(46,53,54,51);(32,33,35,36)(34,38,39,37)(42,50)(46,54)(49,55)(51,53);(40,42,45,50)(41,46,48,54)(43,51,44,53)(47,55,52,49);(32,34,35,39)(33,37,36,38)(40,43,45,44)(41,47,48,52)(42,51,50,53)(46,55,54,49)

Conjugacy classes & character table

899 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2109);