Finite Group Databasebeta

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C₃₁×#3289 #16843222

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

448 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)(32,33,38,44)(34,45,49,60)(35,41,51,59)(36,43,37,42)(39,52,56,48)(40,53,57,50)(46,54,63,55)(47,61,62,58);(32,34,38,49)(33,39,44,56)(35,46,51,63)(36,52,37,48)(40,54,57,55)(41,58,59,61)(42,60,43,45)(47,53,62,50);(32,35)(33,40)(34,46)(36,50)(37,53)(38,51)(39,54)(41,42)(43,59)(44,57)(45,61)(47,52)(48,62)(49,63)(55,56)(58,60);(32,35)(33,41)(34,47)(36,53)(37,50)(38,51)(39,55)(40,42)(43,57)(44,59)(45,61)(46,52)(48,63)(49,62)(54,56)(58,60)

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, 2021);