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C₂×#39415 #7636626

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

Aliases

Subgroups

9382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7543822);