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C₂×#52250 #7633579

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

Aliases

Subgroups

5896 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540775);