Finite Group Databasebeta

?

← Prev (#6345020) Next (#6345022) →

C₂×#18037 #6345021

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

Aliases

Subgroups

1878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252217);