Finite Group Databasebeta

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C₃₁×#3191 #16843124

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

424 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)(34,38)(35,37)(36,39)(40,41)(42,49)(43,47)(44,52)(45,48)(46,50)(51,54)(53,55);(32,34)(33,36)(35,39)(37,38);(34,39)(36,38)(40,42)(41,46)(43,50)(44,53)(45,51)(47,54)(48,55)(49,52);(33,37)(36,38)(40,43,45,44)(41,47,48,52)(42,50,51,53)(46,54,55,49)

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, 1923);