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C₂×#17961 #6344786

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

Aliases

Subgroups

1686 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6251982);