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C₂×#23527 #6431936

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

Aliases

Subgroups

4638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339132);