Finite Group Databasebeta

?

← Prev (#7636661) Next (#7636663) →

C₂×#39357 #7636662

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

Aliases

Subgroups

11938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7543858);