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C₂×#60170 #10574154

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

Aliases

Subgroups

10630 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)(9,14)(10,15)(11,20)(12,16)(13,17)(18,21)(19,22);(7,9)(8,13)(10,17)(11,19)(12,18)(14,20)(15,21)(16,22);(3,5,6,4)(7,9)(8,14)(10,19)(11,17)(12,18)(13,20)(15,22)(16,21);(7,10,12,11)(8,15,16,20)(9,17,18,19)(13,21,22,14);(8,16)(13,22)(14,21)(15,20)

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, 10481350);