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C₂×#10766 #353343

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

Aliases

Subgroups

4062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260539);