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C₂×#11415 #479964

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

Aliases

Subgroups

570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 387160);