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C₂×#57143 #8100498

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

Aliases

Subgroups

6250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,7)(8,10)(19,20)(21,25)(22,29)(23,24)(26,30)(27,33)(28,31)(32,34);(5,9)(8,10)(11,12,15,17)(13,14,18,16)(20,24)(25,31)(26,29)(32,33);(3,4,6,7)(5,8,9,10)(11,13,15,18)(12,16,17,14)(19,21,23,28)(20,25,24,31)(22,27,30,34)(26,32,29,33);(3,4)(5,8)(6,7)(9,10)(11,13)(12,14)(15,18)(16,17)(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)(12,13)(15,16)(17,18)(19,22)(20,26)(21,27)(23,30)(24,29)(25,32)(28,34)(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, 8007694);