Finite Group Databasebeta

?

← Prev (#7623703) Next (#7623705) →

C₂×#33892 #7623704

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

Aliases

Subgroups

1794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530900);