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C₂×#37139 #7634431

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

Aliases

Subgroups

5526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,7)(6,9)(8,10)(11,12)(13,17)(14,15)(16,18)(21,25)(23,26);(4,5)(8,9)(12,15)(16,17)(19,20,22,24)(21,23,25,26);(11,12)(13,16)(14,15)(17,18)(19,21,22,25)(20,23,24,26);(3,5,7,4)(6,9,10,8)(11,13)(12,16)(14,18)(15,17);(3,6)(4,8)(5,9)(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, 7541627);