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C₂×#13511 #499419

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

Aliases

Subgroups

586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406615);