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C₂×#25864 #6446614

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

Aliases

Subgroups

5058 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)(17,21)(18,20)(19,22);(3,4)(5,6)(7,9,11,10)(8,12,14,13)(16,20)(17,22);(4,6)(7,9,11,10)(8,13,14,12)(15,17,21,16,18,22,19,20);(7,10,11,9)(8,13,14,12)(16,20)(17,22)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6353810);