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C₂×#47204 #7700828

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

Aliases

Subgroups

8174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7608024);