Finite Group Databasebeta

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C₃₇×#576 #14557241

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

268 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)(41,43)(42,46)(45,49)(47,51)(48,50)(52,53);(39,43)(41,49)(44,50)(45,46)(48,53)(51,52);(38,40)(39,44)(41,48)(42,47)(43,50)(45,52)(46,51)(49,53);(40,47)(44,51)(48,53)(50,52)

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, 257);