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C₂×#17404 #6342638

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

Aliases

Subgroups

3144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6249834);