Finite Group Databasebeta

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C₃₁×#3376 #16843309

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

346 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)(40,41,43,47)(42,49,50,45)(44,46,52,48)(51,53,55,54);(32,33,35,36)(34,38,39,37)(40,42,43,50)(41,45,47,49)(44,51,52,55)(46,54,48,53);(41,46)(42,50)(44,52)(45,53)(47,48)(49,54);(32,34,35,39)(33,37,36,38)(42,50)(45,49)(51,55)(53,54)

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, 2108);