Finite Group Databasebeta

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C₃₁×#2638 #16842571

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

520 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)(37,40)(41,43)(44,45)(46,48)(47,49)(50,51);(33,35)(37,40)(41,43)(45,46)(49,50);(32,33)(34,35)(36,37)(38,41)(39,40)(42,43)(44,46,48,45)(47,49,51,50);(36,38,39,42)(37,41,40,43)(44,47)(45,49)(46,50)(48,51)

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, 1370);