Finite Group Databasebeta

?

← Prev (#7635876) Next (#7635878) →

C₂×#38444 #7635877

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

Aliases

Subgroups

6894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4)(5,9)(6,7)(8,10)(19,20,23,24)(21,26,25,22);(4,7)(8,9)(12,15)(16,18)(20,24)(21,25);(11,12)(13,16)(14,15)(17,18)(19,21,23,25)(20,22,24,26);(3,5,6,10)(4,8,7,9)(11,13,14,17)(12,16,15,18)(19,22)(20,25)(21,24)(23,26);(3,4)(5,8)(6,7)(9,10)(11,12)(13,16)(14,15)(17,18)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7543073);