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C₂×#17968 #6344796

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

Aliases

Subgroups

1758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251992);