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C₂×#17974 #6344803

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

Aliases

Subgroups

1666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251999);