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C₃₇×#490 #14557155

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

110 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)(47,52)(48,53)(49,50);(39,42)(43,45)(46,47,49,52,51,53,50,48);(38,40,41,44)(39,43,42,45)(46,48,49,47,51,52,50,53)

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, 171);