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C₂×#62108 #10579355

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

Aliases

Subgroups

6398 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)(19,20,23,27)(21,24,28,32)(22,25,30,26)(29,33,34,31);(3,5)(4,8)(6,13)(7,12)(9,16)(10,11)(14,17)(15,18)(19,21)(20,24)(22,29)(23,28)(25,33)(26,31)(27,32)(30,34);(20,25)(21,28)(22,30)(24,31)(26,27)(32,33);(5,12)(8,11)(13,18)(16,17);(3,6,7,15)(4,9,10,14)(5,13,12,18)(8,16,11,17)

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, 10486551);