Finite Group Databasebeta

?

← Prev (#14557204) Next (#14557206) →

C₃₇×#540 #14557205

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 53 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)(40,44)(41,42)(43,45)(47,50)(48,52);(39,42)(43,44)(46,47,49,50)(48,51,52,53);(38,39)(40,43)(41,42)(44,45)(46,47)(48,51)(49,50)(52,53);(38,40,41,45)(39,43,42,44)(46,48,49,52)(47,51,50,53)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 221);