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C₂×#21779 #6374191

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

Aliases

Subgroups

4376 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6281387);