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C₂×#20116 #6359447

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

Aliases

Subgroups

1564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6266643);