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C₂×#10951 #354119

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

Aliases

Subgroups

2850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 261315);