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C₂×#7256 #127507

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

Aliases

Subgroups

834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 34 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 34703);