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C₂×#57756 #8101802

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

Aliases

Subgroups

5314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8008998);