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C₂×#11356 #358609

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

Aliases

Subgroups

1622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265805);