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C₂×#52275 #7633593

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

Aliases

Subgroups

5988 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,7,9)(5,8,6,10)(11,12)(13,16)(14,15)(17,18)(19,20,22,24)(21,23,25,26);(3,4)(5,8)(6,10)(7,9)(21,25)(23,26);(3,5,7,6)(4,8,9,10)(12,15)(16,18)(19,21,22,25)(20,23,24,26);(3,6,7,5)(4,8,9,10)(12,15)(16,18);(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, 7540789);