Finite Group Databasebeta

?

← Prev (#7705254) Next (#7705256) →

C₂×#49552 #7705255

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

Aliases

Subgroups

9392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7612451);