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C₂×#10757 #353452

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

Aliases

Subgroups

4030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260648);