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C₂×#10767 #353344

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

Aliases

Subgroups

3982 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260540);