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C₂×#23535 #6431948

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

Aliases

Subgroups

4678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339144);