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C₂×#34411 #7626060

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

Aliases

Subgroups

10110 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)(9,13)(10,12)(11,14)(16,19)(17,21);(7,8,10,12)(9,11,14,13)(15,16,18,19)(17,20,21,22);(3,5,6,4)(15,16)(17,20)(18,19)(21,22);(7,8)(9,11)(10,12)(13,14)(15,16)(17,20)(18,19)(21,22);(7,9,10,14)(8,11,12,13)(15,17,18,21)(16,20,19,22)

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, 7533256);