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C₃₇×#489 #14557154

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

100 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)(40,43)(41,42)(44,45)(46,47)(48,50)(49,51)(52,53);(39,42)(43,45)(46,48,51,53,52,49,50,47);(38,40,41,44)(39,43,42,45)(46,49,50,53,52,48,51,47)

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, 170);