Finite Group Databasebeta

?

← Prev (#7667265) Next (#7667267) →

C₂×#43030 #7667266

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

Aliases

Subgroups

7926 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)(9,12)(10,11)(13,14)(17,21)(20,22);(8,11)(12,14)(15,16)(17,22)(18,19)(20,21);(3,4)(5,6)(16,19)(20,22);(7,8)(9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22);(7,9,10,13)(8,12,11,14)(15,17)(16,20)(18,21)(19,22)

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, 7574462);