Finite Group Databasebeta

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C₃₁×#3081 #16843014

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

398 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)(32,33,35,37)(34,38,39,36)(40,41)(42,45)(43,46)(44,48)(47,51)(49,53)(50,52)(54,55);(32,34,35,39)(33,36,37,38)(40,42)(41,45)(43,50)(44,49)(46,52)(47,54)(48,53)(51,55);(41,46)(43,51)(45,52)(47,48)(50,55)(53,54);(42,49)(45,53)(50,55)(52,54)

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, 1813);