Finite Group Databasebeta

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C₃₁×#2590 #16842523

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 55 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)(33,36)(37,39)(40,41,44,45)(42,47,46,43)(50,54)(53,55);(33,36)(37,39)(41,45)(42,46)(48,49,52,51)(50,53,54,55);(32,33,35,36)(34,37,38,39)(40,42,44,46)(41,43,45,47)(48,50)(49,53)(51,55)(52,54);(32,34,35,38)(33,37,36,39)(40,43)(41,46)(42,45)(44,47)(48,51,52,49)(50,55,54,53)

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1322);