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C₂×#17399 #6342632

• 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)(19,20,23,28,24,27,22,26)(21,25,29,32,30,33,31,34);(3,5)(4,8)(6,12)(7,13)(9,15)(10,11)(14,18)(16,17)(19,21)(20,25)(22,31)(23,29)(24,30)(26,34)(27,33)(28,32);(19,22,24,23)(20,26,27,28)(21,29,30,31)(25,32,33,34);(3,6,7,14)(4,9,10,16)(5,12,13,18)(8,15,11,17)(20,27)(25,33)(26,28)(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, 6249828);