Finite Group Databasebeta

?

← Prev (#17992106) Next (#17992108) →

C₃₇×#3289 #17992107

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(38,39,44,50)(40,51,55,66)(41,47,57,65)(42,49,43,48)(45,58,62,54)(46,59,63,56)(52,60,69,61)(53,67,68,64);(38,40,44,55)(39,45,50,62)(41,52,57,69)(42,58,43,54)(46,60,63,61)(47,64,65,67)(48,66,49,51)(53,59,68,56);(38,41)(39,46)(40,52)(42,56)(43,59)(44,57)(45,60)(47,48)(49,65)(50,63)(51,67)(53,58)(54,68)(55,69)(61,62)(64,66);(38,41)(39,47)(40,53)(42,59)(43,56)(44,57)(45,61)(46,48)(49,63)(50,65)(51,67)(52,58)(54,69)(55,68)(60,62)(64,66)

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2021);