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C₂×#17916 #6344623

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

Aliases

Subgroups

1778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6251819);