Finite Group Databasebeta

?

← Prev (#7705372) Next (#7705374) →

C₂×#49578 #7705373

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

Aliases

Subgroups

8752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,5,6)(7,8)(9,13)(10,14)(11,12);(7,9)(8,10)(11,14)(12,13)(16,19)(17,21);(3,4)(5,6)(8,12)(9,14)(15,16,18,19)(17,20,21,22);(7,9)(8,13)(10,12)(11,14)(15,16)(17,20)(18,19)(21,22);(7,10,11,13)(8,9,12,14)(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, 7612569);