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C₂×#45108 #7669590

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

Aliases

Subgroups

9386 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)(10,11)(12,14)(16,17)(20,21);(7,8)(9,13)(10,11)(12,14)(15,16,19,17)(18,21,22,20);(3,4)(5,6)(8,11)(12,13)(15,17,19,16)(18,21,22,20);(7,8)(9,12)(10,11)(13,14)(15,18)(16,20)(17,21)(19,22);(7,9,10,14)(8,12,11,13)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7576786);