Finite Group Databasebeta

?

← Prev (#7635531) Next (#7635533) →

C₂×#38252 #7635532

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

Aliases

Subgroups

6438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542728);