Finite Group Databasebeta

?

← Prev (#7633951) Next (#7633953) →

C₂×#36747 #7633952

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

Aliases

Subgroups

7602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,9)(6,10)(7,8)(13,17)(16,18)(19,20,23,24)(21,26,25,22);(4,8)(5,10)(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)(4,6)(7,10)(8,9)(11,12)(13,16)(14,15)(17,18)(19,22)(20,25)(21,24)(23,26);(3,6)(4,5)(7,9)(8,10)(11,13)(12,16)(14,17)(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, 7541148);