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C₂×#37778 #7634958

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

Aliases

Subgroups

10206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542154);