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C₂×#17499 #6343005

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

Aliases

Subgroups

3208 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,13)(6,10)(7,11)(8,12)(9,14)(15,17)(16,18)(19,20,22,26,23,25,29,32)(21,24,28,31,27,30,33,34);(3,5)(4,9)(6,14)(7,16)(8,15)(10,17)(11,13)(12,18)(19,21)(20,24)(22,28)(23,27)(25,30)(26,31)(29,33)(32,34);(3,6,8,7)(4,10,12,11)(5,14,15,16)(9,17,18,13)(21,27)(24,30)(28,33)(31,34);(3,6,8,7)(4,11,12,10)(5,14,15,16)(9,13,18,17)(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, 6250201);