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C₂×#20360 #6369767

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

Aliases

Subgroups

7478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6276963);