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C₂×#11121 #357789

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

Aliases

Subgroups

4074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264985);