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C₂×#13522 #499442

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

Aliases

Subgroups

562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406638);