Finite Group Databasebeta

?

← Prev (#14557227) Next (#14557229) →

C₃₇×#563 #14557228

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 61 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)(39,42)(40,44)(46,47,51,49)(48,54,56,52)(50,57,59,53)(55,60,58,61);(39,42)(43,45)(46,48,51,56)(47,52,49,54)(50,58,59,55)(53,61,57,60);(38,39)(40,43)(41,42)(44,45)(46,49,51,47)(48,52,56,54)(50,57,59,53)(55,60,58,61);(38,40)(39,43)(41,44)(42,45)(46,50)(47,53)(48,55)(49,57)(51,59)(52,60)(54,61)(56,58)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 244);