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C₂×#37769 #7634978

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

Aliases

Subgroups

10906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542174);