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C₂×#13046 #494586

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

Aliases

Subgroups

1947 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401782);