Finite Group Databasebeta

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C₃₁×#2575 #16842508

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

412 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)(32,33,36,35)(34,38,39,37)(40,41,44,45)(42,43,46,47)(50,54)(53,55);(34,39)(37,38)(41,45)(42,46)(48,49,52,51)(50,53,54,55);(32,34)(33,37)(35,38)(36,39)(40,42)(41,43)(44,46)(45,47)(48,50)(49,53)(51,55)(52,54);(32,35,36,33)(34,38,39,37)(40,43)(41,42)(44,47)(45,46)(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, 1307);