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C₂×#21781 #6374193

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

Aliases

Subgroups

4332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6281389);