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C₂×#17922 #6344631

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

Aliases

Subgroups

1954 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)(7,10)(11,14)(12,17)(13,15)(16,18)(19,20,22,26,23,25,29,32)(21,24,27,31,28,30,33,34);(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)(19,21,22,27,23,28,29,33)(20,24,26,31,25,30,32,34);(4,10)(5,12)(8,11)(13,18)(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, 6251827);