Finite Group Databasebeta

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C₃₁×#3276 #16843209

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 51 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)(34,35)(36,37,41,39)(38,44,47,51)(40,49,50,43)(42,45,48,46);(36,38,41,47)(37,42,39,48)(40,45,50,46)(43,51,49,44);(33,35)(36,39,41,37)(38,42,47,48)(40,49,50,43)(44,45,51,46);(38,45)(40,50)(42,51)(43,49)(44,48)(46,47)

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, 2008);