Finite Group Databasebeta

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C₃₁×#2790 #16842723

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

408 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)(34,38)(40,41)(42,46)(43,44)(45,47)(48,49,51,53)(50,54,55,52);(33,36)(37,39)(41,44)(42,47)(48,49)(50,54)(51,53)(52,55);(32,33,35,36)(34,37,38,39)(40,41)(42,45)(43,44)(46,47);(32,34,35,38)(33,37,36,39)(40,42,43,47)(41,45,44,46)(48,50,51,55)(49,52,53,54)

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, 1522);