Finite Group Databasebeta

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C₃₁×#2495 #16842428

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

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, 1227);