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C₂×#12865 #493892

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

Aliases

Subgroups

860 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401088);