Finite Group Databasebeta

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C₃₁×#2612 #16842545

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

388 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)(48,49,52,55)(50,54,51,53);(33,36)(37,38)(40,41,43,45)(42,44,46,47)(48,50,52,51)(49,53,55,54);(32,33)(34,37)(35,36)(38,39)(40,41)(42,44)(43,45)(46,47)(48,51,52,50)(49,54,55,53);(32,34,35,39)(33,37,36,38)(40,42,43,46)(41,44,45,47)(48,49)(50,53)(51,54)(52,55)

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, 1344);