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C₂×#35884 #7629283

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

Aliases

Subgroups

5746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536479);