Finite Group Databasebeta

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C₃₇×#585 #14557250

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 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)(40,46)(41,45)(42,44)(43,47)(48,52)(49,51)(50,53);(38,40)(39,43)(41,48)(42,47)(44,46)(45,50)(49,53)(51,52);(40,47)(43,46)(48,53)(50,52);(39,44)(43,46)(45,51)(50,52);(38,41,42,49)(39,45,44,51)(40,48,47,53)(43,50,46,52)

Conjugacy classes & character table

1258 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 266);