Finite Group Databasebeta

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C₃₁×#2717 #16842650

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

512 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)(38,39)(40,41)(42,43)(45,48)(49,50);(33,35)(37,41)(39,43)(44,45,47,48)(46,50,51,49);(32,33)(34,35)(36,38,40,42)(37,39,41,43)(44,45)(46,49)(47,48)(50,51);(36,39)(37,42)(38,41)(40,43)(44,46)(45,49)(47,51)(48,50)

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, 1449);