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C₃₁×#3544 #16843477

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1004 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)(41,45)(43,51)(46,48)(49,55);(33,36)(37,39)(40,41,44,45)(42,48,50,46)(43,47,51,52)(49,54,55,53);(32,33,35,36)(34,37,38,39);(32,34)(33,37)(35,38)(36,39)(40,42,44,50)(41,46,45,48)(43,49,51,55)(47,53,52,54);(40,43)(41,47)(42,49)(44,51)(45,52)(46,53)(48,54)(50,55)

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, 2276);