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C₂×#47844 #7703943

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

Aliases

Subgroups

10510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7611139);