Finite Group Databasebeta

?

← Prev (#6437498) Next (#6437500) →

C₂×#23871 #6437499

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

Aliases

Subgroups

6406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344695);