Finite Group Databasebeta

?

← Prev (#353527) Next (#353529) →

C₂×#10819 #353528

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

Aliases

Subgroups

1986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260724);