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C₂×#21740 #6374104

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

Aliases

Subgroups

6710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6281300);