Finite Group Databasebeta

?

← Prev (#492855) Next (#492857) →

C₂×#12557 #492856

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

Aliases

Subgroups

1850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400052);