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C₂×#62194 #10579445

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

Aliases

Subgroups

6342 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)(19,20,25,28)(21,26,22,31)(23,29,24,33)(27,30,34,32);(3,5)(4,8)(6,13)(7,12)(9,16)(10,11)(14,17)(15,18)(19,21,25,22)(20,26,28,31)(23,32,24,30)(27,33,34,29);(19,22,25,21)(20,27,28,34)(23,32,24,30)(26,33,31,29);(5,12)(8,11)(13,18)(16,17)(20,28)(26,31)(27,34)(29,33);(3,6,7,15)(4,9,10,14)(5,13,12,18)(8,16,11,17)(19,23,25,24)(20,29,28,33)(21,30,22,32)(26,34,31,27)

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, 10486641);