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C₃₁×#3236 #16843169

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

324 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 63 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)(34,40)(35,38)(36,39)(37,42)(41,46)(43,45)(44,47)(48,49,52,56)(50,53,57,61)(51,54,59,55)(58,62,63,60);(32,34,36,42)(33,37,39,40)(35,43,44,41)(38,46,47,45)(48,50)(49,53)(51,58)(52,57)(54,62)(55,60)(56,61)(59,63);(32,35,36,44)(33,38,39,47)(34,41,42,43)(37,45,40,46)(49,54)(50,57)(51,59)(53,60)(55,56)(61,62);(33,39)(37,40)(38,47)(45,46)

Conjugacy classes & character table

806 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1968);