Finite Group Databasebeta

?

← Prev (#17990230) Next (#17990232) →

C₃₇×#1413 #17990231

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 69 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)(38,39,41,46,43,48,55,65)(40,49,51,67,50,66,68,63)(42,47,57,64,58,45,54,62)(44,59,60,52,61,53,69,56);(38,40,43,50)(39,44)(41,53,55,59)(42,56,58,52)(45,49)(46,63)(47,66)(48,61)(51,54,68,57)(60,62)(64,69)(65,67)

Conjugacy classes & character table

518 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 145);