Finite Group Databasebeta

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C₃₇×#564 #14557229

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 69 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)(40,46)(41,49)(43,47)(44,51)(54,55,58,61)(56,59,64,62)(57,65,66,60)(63,68,69,67);(38,39,42,45)(40,47,46,43)(41,44,49,51)(48,53,52,50)(54,55)(56,62)(57,65)(58,61)(59,64)(60,66)(63,67)(68,69);(38,40,42,46)(39,43,45,47)(41,48,49,52)(44,50,51,53)(54,56)(55,59)(57,63)(58,64)(60,67)(61,62)(65,68)(66,69);(38,41)(39,44)(40,48)(42,49)(43,50)(45,51)(46,52)(47,53)(54,57,58,66)(55,60,61,65)(56,63,64,69)(59,67,62,68)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 245);