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C₂×#59392 #7665865

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

Aliases

Subgroups

8538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573061);