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C₂×#62205 #10579457

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

Aliases

Subgroups

6332 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)(19,20,24,29)(21,31,22,26)(23,30,25,28)(27,32,34,33);(3,5)(4,8)(6,13)(7,12)(9,16)(10,11)(14,17)(15,18)(19,21,24,22)(20,26,29,31)(23,33,25,32)(27,30,34,28);(19,22,24,21)(20,27,29,34)(23,33,25,32)(26,30,31,28);(5,12)(8,11)(13,18)(16,17);(3,6,7,15)(4,9,10,14)(5,13,12,18)(8,16,11,17)(19,23,24,25)(20,28,29,30)(21,32,22,33)(26,34,31,27)

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, 10486653);