Finite Group Databasebeta

?

← Prev (#7628834) Next (#7628836) →

C₂×#35466 #7628835

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

Aliases

Subgroups

9810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536031);