Finite Group Databasebeta

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C₅×#6867 #11925940

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,3,4,5)(6,7,9,8,10,12,11,13,14)(15,16,19)(17,23,27)(18,22,28)(20,29,25)(21,32,26)(24,34,37)(30,40,41)(31,39,36)(33,38,35);(15,17,24,18,25,35,26,36,41)(16,20,30,22,31,34,21,23,33)(19,27,37,28,29,38,32,39,40)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 14);