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C₂×#37347 #7634721

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

Aliases

Subgroups

5358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7541917);