Finite Group Databasebeta

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C₃₁×#3268 #16843201

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 51 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)(34,35)(37,41)(39,47)(42,48)(43,44)(45,51)(49,50);(36,37,40,44)(38,42,46,50)(39,43,47,41)(45,49,51,48);(33,35)(36,38,40,46)(37,42,44,50)(39,45,47,51)(41,48,43,49);(37,43)(39,47)(41,44)(42,49)(45,51)(48,50)

Conjugacy classes & character table

899 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2000);