Finite Group Databasebeta

?

← Prev (#7629956) Next (#7629958) →

C₂×#36305 #7629957

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

Aliases

Subgroups

6786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537153);