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C₂×C₄×#575 #10574151

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

Aliases

Subgroups

10990 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)(9,16)(10,15)(11,19)(12,14)(13,17)(18,22)(20,21);(7,9)(8,13)(10,17)(11,20)(12,18)(14,21)(15,22)(16,19);(8,14)(13,21)(15,19)(16,22);(7,10,12,11)(8,15,14,19)(9,17,18,20)(13,22,21,16)

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, 10481347);