Finite Group Databasebeta

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C₃₁×#2693 #16842626

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

568 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)(38,41)(39,40)(42,43)(45,46)(49,50);(33,35)(37,39)(38,42)(44,45,48,46)(47,50,51,49);(32,33)(34,35)(36,38,40,42)(37,41,39,43)(44,46,48,45)(47,50,51,49);(36,39,40,37)(38,43,42,41)(44,47,48,51)(45,49,46,50)

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, 1425);