Finite Group Databasebeta

?

← Prev (#493755) Next (#493757) →

C₂×#12813 #493756

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

Aliases

Subgroups

1370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400952);