Finite Group Databasebeta

?

← Prev (#11925934) Next (#11925936) →

C₅×#6862 #11925935

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 59 points:

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

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 9);