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C₂×#26178 #6438412

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

Aliases

Subgroups

2926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6345608);