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C₂×#43012 #7667146

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

Aliases

Subgroups

9810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8)(9,13)(10,14)(11,12)(17,21)(20,22);(8,12)(9,14)(15,16)(17,22)(18,19)(20,21);(3,4)(5,6)(16,19)(20,22);(7,9,11,14)(8,13,12,10)(15,16)(17,20)(18,19)(21,22);(7,10,11,13)(8,14,12,9)(15,17)(16,20)(18,21)(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, 7574342);