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C₂×#13469 #499309

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

Aliases

Subgroups

760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406505);