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C₂×#62969 #10586314

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

Aliases

Subgroups

32430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 34 points:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493510);