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C₂×#11251 #358107

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

Aliases

Subgroups

1766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265303);