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C₂×#62199 #10579451

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

Aliases

Subgroups

6586 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)(21,24)(22,25)(23,27)(26,30)(28,32)(29,31)(33,34);(3,5)(4,8)(6,13)(7,12)(9,16)(10,11)(14,17)(15,18)(19,21)(20,24)(22,29)(23,28)(25,31)(26,33)(27,32)(30,34);(20,25)(22,30)(24,31)(26,27)(29,34)(32,33);(5,12)(8,11)(13,18)(16,17)(21,28)(24,32)(29,34)(31,33);(3,6,7,15)(4,9,10,14)(5,13,12,18)(8,16,11,17)(21,28)(24,32)(29,34)(31,33)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10486647);