Finite Group Databasebeta

?

← Prev (#7669153) Next (#7669155) →

C₂×#44770 #7669154

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

Aliases

Subgroups

8290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7576350);