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C₂×#30412 #7500644

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

Aliases

Subgroups

4048 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7407840);