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C₂×#61713 #10577882

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

Aliases

Subgroups

6652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485078);