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C₅×#6899 #11925972

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 46);