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C₂×#12029 #483416

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

Aliases

Subgroups

476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 390612);