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C₂×#40169 #7637803

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

Aliases

Subgroups

7198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7544999);