Finite Group Databasebeta

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C₃₁×#3490 #16843423

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1328 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 47 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)(34,40)(35,39)(36,38)(37,41)(42,46)(43,45)(44,47);(32,34,36,42)(33,37,38,44)(35,41,43,47)(39,40,45,46);(33,38)(37,44)(39,45)(40,46);(34,41)(37,40)(42,47)(44,46);(33,39)(37,40)(38,45)(44,46)

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, 2222);