Finite Group Databasebeta

?

← Prev (#7704826) Next (#7704828) →

C₂×#48790 #7704827

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

Aliases

Subgroups

8500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7612023);