Finite Group Databasebeta

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C₃₁×#3012 #16842945

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

764 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)(38,43)(39,44)(40,49)(41,45)(42,46)(47,50)(48,51);(36,38)(37,42)(39,46)(40,48)(41,47)(43,49)(44,50)(45,51);(33,35)(36,38)(37,43)(39,48)(40,46)(41,47)(42,49)(44,51)(45,50);(36,39,41,40)(37,44,45,49)(38,46,47,48)(42,50,51,43)

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, 1744);