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C₂×#52986 #8092885

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

Aliases

Subgroups

8834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8000081);