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C₂×#62368 #10578398

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

Aliases

Subgroups

6484 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)(19,20)(21,28)(22,26)(23,32)(24,27)(25,31)(29,34)(30,33);(3,5,7,13)(4,8,10,11)(6,14,15,12)(9,17,18,16)(21,29)(25,33)(28,34)(30,31);(19,21,23,31,24,29,22,30)(20,25,26,28,27,33,32,34);(3,6,7,15)(4,9,10,18)(5,12,13,14)(8,16,11,17);(4,10)(8,11)(9,18)(16,17)(19,22,24,23)(20,26,27,32)(21,30,29,31)(25,28,33,34)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485594);