Finite Group Databasebeta

?

← Prev (#34578) Next (#34580) →

C₂×#2623 #34579

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

Aliases

Subgroups

1501 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27567);