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C₂×#17834 #6344377

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

Aliases

Subgroups

1758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6251573);