Finite Group Databasebeta

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C₃₇×#456 #14557121

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 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)(38,39,43,41)(40,46,49,53)(42,50,52,45)(44,51,47,48);(38,40)(39,44)(41,47)(42,51)(43,49)(45,53)(46,50)(48,52);(38,41,43,39)(40,47,49,44)(42,45,52,50)(46,51,53,48)

Conjugacy classes & character table

592 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 137);