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C₂×#21324 #6372204

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

Aliases

Subgroups

4738 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)(10,11)(12,14)(15,16)(17,18)(19,21)(20,22);(4,6)(8,11)(12,13)(15,17,18,16,20,21,19,22);(7,9,10,14)(8,12,11,13)(15,18,20,19)(16,21,22,17);(15,18,20,19)(16,17,22,21)

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, 6279400);