Finite Group Databasebeta

?

← Prev (#6447750) Next (#6447752) →

C₂×#25949 #6447751

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

Aliases

Subgroups

3888 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6354947);