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C₃₁×#3240 #16843173

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

328 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)(50,58)(51,57)(52,54)(53,56)(55,59)(60,63)(61,62);(32,34,36,42)(33,37,39,40)(35,43,44,41)(38,46,47,45)(49,54)(55,62)(56,57)(58,63);(32,35,36,44)(33,38,39,47)(34,41,42,43)(37,45,40,46)(48,50,52,60)(49,55,54,62)(51,59,53,61)(56,58,57,63);(33,39)(37,40)(38,47)(45,46)(48,51,52,53)(49,56,54,57)(50,59,60,61)(55,58,62,63)

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, 1972);