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C₂×#17659 #6343779

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

Aliases

Subgroups

3236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6250975);