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C₂×#34417 #7626027

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

Aliases

Subgroups

7850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7533223);