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C₂×#52914 #8092735

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

Aliases

Subgroups

6122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

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, 7999931);