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C₂×#60168 #10574152

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

Aliases

Subgroups

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481348);