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C₃₁×#3561 #16843494

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1032 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 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)(34,38)(40,41,44,45)(42,48,49,46)(43,51,52,47)(50,53,55,54);(33,36)(37,39)(41,45)(42,49)(47,51)(50,55);(32,33)(34,37)(35,36)(38,39)(40,41)(42,46)(43,47)(44,45)(48,49)(50,53)(51,52)(54,55);(32,34,35,38)(33,37,36,39)(40,42,44,49)(41,46,45,48)(43,50,52,55)(47,53,51,54);(40,43,44,52)(41,47,45,51)(42,50,49,55)(46,53,48,54)

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, 2293);