Finite Group Databasebeta

?

← Prev (#7668557) Next (#7668559) →

C₂×#43900 #7668558

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

Aliases

Subgroups

9596 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)(17,21)(19,22);(8,12)(9,14)(15,16)(17,22)(18,20)(19,21);(3,4)(5,6)(15,16,18,20)(17,19,21,22);(7,9,11,14)(8,13,12,10)(15,16)(17,19)(18,20)(21,22);(7,10,11,13)(8,14,12,9)(15,17)(16,19)(18,21)(20,22)

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, 7575754);