Finite Group Databasebeta

?

← Prev (#493785) Next (#493787) →

C₂×#12823 #493786

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

Aliases

Subgroups

1158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

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, 400982);