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C₂×#10950 #354041

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

Aliases

Subgroups

2818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 261237);