Finite Group Databasebeta

?

← Prev (#20676) Next (#20678) →

C₂×#1816 #20677

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

Aliases

Subgroups

687 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

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, 13665);