Finite Group Databasebeta

?

← Prev (#6444229) Next (#6444231) →

C₂×#25425 #6444230

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

Aliases

Subgroups

3160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6351426);