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C₂×#2722 #52145

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

Aliases

Subgroups

1231 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 45133);