Finite Group Databasebeta

?

← Prev (#494899) Next (#494901) →

C₂×#13146 #494900

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 66 points:

(1,2);(3,4,8,14,10,15,9,32)(5,16,19,44,21,45,20,54)(6,22,25,57,27,39,26,59)(7,28,29,34,31,60,30,13)(11,33,36,53,37,52,43,18)(12,38,40,23,41,58,56,24)(17,46,49,62,51,64,50,35)(42,63,65,47,55,61,66,48);(3,5,7,18,8,19,29,33,10,21,31,53,9,20,30,52)(4,11,34,45,32,43,28,44,15,37,13,16,14,36,60,54)(6,17,23,47,25,49,58,61,27,51,24,48,26,50,38,63)(12,35,22,55,56,64,59,65,41,62,39,42,40,46,57,66);(3,6,7,23,8,25,29,58,10,27,31,24,9,26,30,38)(4,12,13,39,32,56,60,57,15,41,34,22,14,40,28,59)(5,17,18,47,19,49,33,61,21,51,53,48,20,50,52,63)(11,35,16,42,43,64,54,66,37,62,45,55,36,46,44,65)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402096);