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C₂×#24196 #6448790

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

Aliases

Subgroups

4868 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6355986);