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C₂×#61792 #10577967

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

Aliases

Subgroups

6462 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)(19,20,25,30)(21,32,33,27)(22,34,23,28)(24,31,26,29);(3,5)(4,8)(6,12)(7,13)(9,15)(10,11)(14,18)(16,17)(19,21,25,33)(20,27,30,32)(22,24,23,26)(28,31,34,29);(3,6,7,14)(4,9,10,16)(5,12,13,18)(8,15,11,17)(19,22,25,23)(20,27,30,32)(21,24,33,26)(28,29,34,31);(5,13)(8,11)(12,18)(15,17)(19,23,25,22)(20,28,30,34)(21,24,33,26)(27,29,32,31);(4,10)(8,11)(9,16)(15,17)(19,24,25,26)(20,29,30,31)(21,22,33,23)(27,34,32,28)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485163);