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C₂×#25798 #6443339

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

Aliases

Subgroups

4914 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6350535);