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C₂×#52285 #7633612

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

Aliases

Subgroups

5810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540808);