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C₂×#12686 #493346

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

Aliases

Subgroups

3202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400542);