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C₃₁×#2772 #16842705

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

378 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)(34,38)(35,36)(37,39)(41,42)(45,46)(48,49,52,55)(50,53,54,51);(33,36)(34,39)(40,41,44,42)(43,46,47,45)(48,50,52,54)(49,53,55,51);(32,33)(34,37)(35,36)(38,39)(40,42,44,41)(43,46,47,45)(48,51,52,53)(49,54,55,50);(32,34,35,39)(33,37,36,38)(40,43,44,47)(41,45,42,46)(48,49)(50,53)(51,54)(52,55)

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, 1504);