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C₂×#17827 #6344369

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

Aliases

Subgroups

1742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251565);