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C₂×#59414 #7666198

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

Aliases

Subgroups

10356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573394);