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C₂×#52252 #7633576

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

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, 7540772);