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C₂×#44948 #7669449

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

Aliases

Subgroups

8154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7576645);