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C₂×#13642 #512734

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

Aliases

Subgroups

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 419930);