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C₂×C₄×#413 #6369822

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

Aliases

Subgroups

5414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6277018);