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C₂×#17963 #6344788

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

Aliases

Subgroups

1730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6251984);