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C₂×#52169 #7633495

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

Aliases

Subgroups

8402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540691);