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C₂×#54183 #8103521

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

Aliases

Subgroups

7544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4,6,7)(5,9,10,8)(11,12)(13,16)(14,15)(17,18)(20,24)(22,26);(4,7)(5,10)(11,13,15,18)(12,16,14,17)(19,20,23,24)(21,26,25,22);(4,7)(8,9)(12,14)(16,17)(20,24)(21,25);(3,4)(5,8)(6,7)(9,10)(11,14,15,12)(13,17,18,16)(19,21,23,25)(20,22,24,26);(3,5)(4,8)(6,10)(7,9)(11,13)(12,16)(14,17)(15,18)(19,22)(20,25)(21,24)(23,26)

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, 8010717);