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C₃₁×#3509 #16843442

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

992 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)(34,38)(36,39)(40,41,44,47)(42,45,50,48)(43,51,52,46)(49,54,55,53);(32,33,35,37)(34,36,38,39)(40,41)(42,48)(43,46)(44,47)(45,50)(49,54)(51,52)(53,55);(32,34,35,38)(33,36,37,39);(40,42)(41,45)(43,49)(44,50)(46,53)(47,48)(51,54)(52,55);(40,43,44,52)(41,46,47,51)(42,49,50,55)(45,53,48,54)

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2241);