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C₂×#18014 #6344916

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

Aliases

Subgroups

1856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252112);