Finite Group Databasebeta

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C₃₁×#2696 #16842629

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

562 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)(36,37,40,39)(38,42,43,41)(44,45)(46,49)(47,51)(48,50);(33,35)(37,39)(38,43)(44,46,48,51)(45,49,50,47);(32,33)(34,35)(36,38,40,43)(37,41,39,42)(44,46)(45,47)(48,51)(49,50);(36,39,40,37)(38,42,43,41)(44,47)(45,46)(48,49)(50,51)

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, 1428);