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C₂×#21080 #6371673

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

Aliases

Subgroups

3178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278869);