Finite Group Databasebeta

?

← Prev (#7635081) Next (#7635083) →

C₂×#37737 #7635082

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

Aliases

Subgroups

8698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542278);