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C₂×#11456 #480041

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

Aliases

Subgroups

994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 387237);