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C₂×#61766 #10577939

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

Aliases

Subgroups

6754 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,11)(6,9)(7,10)(8,13)(12,17)(14,16)(15,18)(19,20)(21,24)(22,25)(23,27)(26,30)(28,32)(29,31)(33,34);(3,5)(4,8)(6,12)(7,13)(9,15)(10,11)(14,18)(16,17)(19,21,23,28)(20,24,27,32)(22,29,30,34)(25,31,26,33);(3,6,7,14)(4,9,10,16)(5,12,13,18)(8,15,11,17)(20,25)(22,30)(24,31)(26,27)(29,34)(32,33);(5,13)(8,11)(12,18)(15,17)(21,28)(24,32)(29,34)(31,33);(4,10)(8,11)(9,16)(15,17)(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, 10485135);