Finite Group Databasebeta

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C₃₁×#2691 #16842624

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

554 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)(36,37)(38,39)(40,41)(42,43)(44,45)(46,50)(47,49)(48,51);(33,35)(37,41)(39,42)(44,45,47,49)(46,50,51,48);(32,33)(34,35)(36,38)(37,42)(39,41)(40,43)(44,45)(46,48)(47,49)(50,51);(36,39,40,42)(37,38,41,43)(44,46,47,51)(45,48,49,50)

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, 1423);