Finite Group Databasebeta

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C₃₁×#2627 #16842560

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

508 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)(36,37)(38,40)(39,41)(42,43)(44,45,48,51)(46,49,50,47);(33,35)(36,37,39,41)(38,40,43,42)(44,46)(45,49)(47,51)(48,50);(32,33)(34,35)(36,37)(38,42)(39,41)(40,43)(44,47,48,49)(45,50,51,46);(36,38)(37,40)(39,43)(41,42)

Conjugacy classes & character table

992 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1359);