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C₂×#17838 #6344382

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

Aliases

Subgroups

1688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251578);