Finite Group Databasebeta

?

← Prev (#7634673) Next (#7634675) →

C₂×#37284 #7634674

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

Aliases

Subgroups

7294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541870);