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C₃₁×#2743 #16842676

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 55 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)(32,33,36,34)(35,38,39,37)(40,41)(42,43)(44,45)(46,47)(48,49)(50,53)(51,55)(52,54);(33,34)(35,39)(41,45)(43,47)(48,50,52,55)(49,53,54,51);(32,34,36,33)(35,38,39,37)(40,42,44,46)(41,43,45,47)(48,50)(49,51)(52,55)(53,54);(32,35)(33,37)(34,38)(36,39)(40,43)(41,46)(42,45)(44,47)(48,51)(49,50)(52,53)(54,55)

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, 1475);