Finite Group Databasebeta

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C₃₁×#3407 #16843340

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

360 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)(32,33,35,40,36,41,45,53,37,39,46,51,47,52,57,61)(34,38,43,49,44,50,56,60,42,48,54,58,55,59,62,63);(32,34)(33,38)(35,43)(36,44)(37,42)(39,48)(40,49)(41,50)(45,56)(46,54)(47,55)(51,58)(52,59)(53,60)(57,62)(61,63);(34,42)(38,48)(43,54)(44,55)(49,58)(50,59)(56,62)(60,63);(33,39)(38,48)(40,51)(41,52)(49,58)(50,59)(53,61)(60,63)

Conjugacy classes & character table

2108 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2139);