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C₂×#17665 #6343785

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

Aliases

Subgroups

3192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

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, 6250981);