Finite Group Databasebeta

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C₃₁×#3492 #16843425

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1124 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)(34,35)(36,37)(38,39)(42,46)(44,47);(33,37)(34,38)(40,41,43,45)(42,44,46,47);(40,42)(41,44)(43,46)(45,47);(32,34,36,38)(33,35,37,39);(32,35)(33,38)(34,37)(36,39)

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, 2224);