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C₂×#34458 #7626093

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

Aliases

Subgroups

8210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7533289);