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C₂×#17395 #6342627

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

Aliases

Subgroups

3252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6249823);