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C₃₁×#3518 #16843451

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1010 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)(37,39)(40,41,46,44)(42,49,43,47)(45,52,53,48)(50,54,51,55);(40,42,46,43)(41,47,44,49)(45,50,53,51)(48,54,52,55);(32,33)(34,37)(35,36)(38,39)(40,43,46,42)(41,47,44,49)(45,51,53,50)(48,54,52,55);(40,44,46,41)(42,47,43,49)(45,52,53,48)(50,54,51,55);(32,34,35,38)(33,37,36,39)(40,45)(41,48)(42,50)(43,51)(44,52)(46,53)(47,54)(49,55)

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, 2250);