Finite Group Databasebeta

?

← Prev (#492884) Next (#492886) →

C₂×#12575 #492885

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

Aliases

Subgroups

2530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400081);