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C₂×#62229 #10579482

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

Aliases

Subgroups

6174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

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, 10486678);