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C₂×#60288 #10574395

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

Aliases

Subgroups

6614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481591);