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C₂×#57982 #8103954

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

Aliases

Subgroups

6100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8011150);