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C₂×#13540 #499557

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

Aliases

Subgroups

542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406753);