Finite Group Databasebeta

?

← Prev (#7629642) Next (#7629644) →

C₂×#35927 #7629643

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

Aliases

Subgroups

13524 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536839);