Finite Group Databasebeta

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C₃₁×#3487 #16843420

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 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)(33,35)(37,38)(40,48)(42,44)(46,51);(36,37,41,38)(39,44,47,42)(40,43,48,45)(46,50,51,49);(32,33)(34,35)(36,38,41,37)(39,44,47,42)(40,45,48,43)(46,50,51,49);(36,39,41,47)(37,42,38,44)(40,46,48,51)(43,49,45,50);(36,40)(37,43)(38,45)(39,46)(41,48)(42,49)(44,50)(47,51)

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2219);