Finite Group Databasebeta

?

← Prev (#7636626) Next (#7636628) →

C₂×#39423 #7636627

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

Aliases

Subgroups

8038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 7543823);