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C₂×#3243 #60857

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

Aliases

Subgroups

871 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53845);