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C₂×#61756 #10577926

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

Aliases

Subgroups

6564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485122);