Finite Group Databasebeta

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C₅×#6897 #11925970

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5)(6,7,11)(8,15,28)(9,13,21)(10,14,22)(12,23,19)(16,25,31)(17,24,32)(18,26,29)(20,27,30)(33,34,37)(35,38,44)(36,40,45)(39,49,43)(41,46,52)(42,48,53)(47,56,51)(50,55,58)(54,59,57);(6,8,16,10,9,17,20,19,18)(7,12,24,14,15,26,27,13,25)(11,21,29,22,23,31,30,28,32)(33,35,41,36,42,50,43,51,57)(34,38,46,40,48,55,39,47,54)(37,44,52,45,53,58,49,56,59);(6,9,18,10,19,16,20,8,17)(7,13,26,14,12,25,27,15,24)(11,21,29,22,23,31,30,28,32)(34,39,40)(37,45,49)(38,47,48)(44,53,56)(46,54,55)(52,58,59)

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, 44);