Finite Group Databasebeta

?

← Prev (#16843057) Next (#16843059) →

C₃₁×#3125 #16843058

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

384 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)(34,37)(35,36)(38,39)(40,41,43,47)(42,49,50,45)(44,46,52,48)(51,54,55,53);(33,36)(37,39)(40,42,43,50)(41,45,47,49)(44,51,52,55)(46,53,48,54);(41,46)(44,52)(45,53)(47,48)(49,54)(51,55);(32,34,35,38)(33,37,36,39)(42,50)(45,49)(51,55)(53,54)

Conjugacy classes & character table

992 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1857);