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C₂×#62508 #10579794

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

Aliases

Subgroups

6268 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

(1,2);(3,4,7,10)(5,11,12,8)(6,14,15,9)(13,16,18,17)(19,20,24,27)(21,25,23,32)(22,29,30,34)(26,28,33,31);(3,5)(4,8)(6,13)(7,12)(9,16)(10,11)(14,17)(15,18)(19,21,24,23)(20,25,27,32)(22,28,30,31)(26,29,33,34);(19,22,23,31,24,30,21,28)(20,26,25,29,27,33,32,34);(5,12)(8,11)(13,18)(16,17)(19,21,24,23)(20,25,27,32)(22,28,30,31)(26,29,33,34);(3,6,7,15)(4,9,10,14)(5,13,12,18)(8,16,11,17)(22,30)(26,33)(28,31)(29,34)

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10486990);