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C₂×C₄×#539 #7625312

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

Aliases

Subgroups

8306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532508);