Finite Group Databasebeta

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C₃₁×#2716 #16842649

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

450 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)(38,42)(44,45,49,51)(46,48,47,50);(33,35)(37,40)(41,43)(44,46,49,47)(45,50,51,48);(32,33)(34,35)(36,37,39,40)(38,41,42,43)(44,47,49,46)(45,50,51,48);(36,38)(37,41)(39,42)(40,43)(44,48,49,50)(45,46,51,47)

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, 1448);