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C₂×#62119 #10579366

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

Aliases

Subgroups

6506 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)(19,20,22,26)(21,28,29,24)(23,25,31,27)(30,32,34,33);(3,5)(4,8)(6,13)(7,12)(9,16)(10,11)(14,17)(15,18)(19,21)(20,24)(22,29)(23,30)(25,33)(26,28)(27,32)(31,34);(20,25)(21,29)(23,31)(24,32)(26,27)(28,33);(5,12)(8,11)(13,18)(16,17)(21,29)(24,28)(30,34)(32,33);(3,6,7,15)(4,9,10,14)(5,13,12,18)(8,16,11,17)(20,26)(24,28)(25,27)(32,33)

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, 10486562);