Finite Group Databasebeta

?

← Prev (#6460210) Next (#6460212) →

C₂×#28958 #6460211

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

Aliases

Subgroups

1968 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6367407);