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C₂×#30416 #7500646

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

Aliases

Subgroups

3950 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)(17,20)(18,21)(19,22);(3,4)(5,6)(7,9)(8,11)(10,14)(12,13)(15,17,19,18)(16,20,22,21);(4,6)(16,21)(17,18)(20,22);(8,12)(9,14)(16,21)(17,18)(20,22)

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, 7407842);