Finite Group Databasebeta

?

← Prev (#6437499) Next (#6437501) →

C₂×#23868 #6437500

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

Aliases

Subgroups

6320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344696);