Finite Group Databasebeta

?

← Prev (#7636691) Next (#7636693) →

C₂×#39376 #7636692

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

Aliases

Subgroups

7758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7543888);