Finite Group Databasebeta

?

← Prev (#11925970) Next (#11925972) →

C₅×#6898 #11925971

• 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)(6,7,10)(8,12,18)(9,13,17)(11,19,16)(14,21,26)(15,22,25)(20,27,24)(23,29,31)(28,32,30)(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);(7,11,13)(10,17,19)(12,20,22)(18,25,27)(21,28,29)(26,31,32)(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);(6,8,14,16,24,30,9,15,23)(7,12,21,11,20,28,13,22,29)(10,18,26,19,27,32,17,25,31)(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, 45);