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C₂×#57294 #8100478

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

Aliases

Subgroups

6716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8007674);