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C₂×#62762 #10586162

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

Aliases

Subgroups

32316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 34 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493358);