Finite Group Databasebeta

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C₃₁×#2690 #16842623

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

456 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)(39,43)(40,42)(44,45,47,49)(46,50,51,48);(33,35)(36,38,40,43)(37,41,42,39)(44,45)(46,50)(47,49)(48,51);(32,33)(34,35)(36,38)(37,39)(40,43)(41,42);(36,39)(37,38)(40,41)(42,43)(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, 1422);