Finite Group Databasebeta

?

← Prev (#7669358) Next (#7669360) →

C₂×#45032 #7669359

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

Aliases

Subgroups

5718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7576555);