Finite Group Databasebeta

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C₅×#6895 #11925968

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 41 points:

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

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, 42);