Finite Group Databasebeta

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C₃₁×#2597 #16842530

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

454 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)(32,33)(34,36)(35,38)(37,39)(40,41,44,43)(42,46,47,45)(49,51)(53,54);(33,34)(37,38)(42,47)(45,46)(48,49,52,51)(50,54,55,53);(32,34,36,33)(35,38,39,37)(40,42,44,47)(41,45,43,46)(48,50,52,55)(49,53,51,54);(32,35)(33,37)(34,38)(36,39)(40,43,44,41)(42,46,47,45)(48,51,52,49)(50,54,55,53)

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, 1329);