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C₂×C₄×#555 #7625397

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

Aliases

Subgroups

9126 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)(9,13)(10,14)(11,12)(16,17)(20,21);(8,12)(10,13)(15,16,19,17)(18,21,22,20);(7,9,11,14)(8,13,12,10)(15,17,19,16)(18,21,22,20);(7,10,11,13)(8,14,12,9)(15,18,19,22)(16,20,17,21)

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532593);