Finite Group Databasebeta

?

← Prev (#7501157) Next (#7501159) →

C₂×#30566 #7501158

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

Aliases

Subgroups

2920 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 7408354);