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C₂×#41005 #7638753

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

Aliases

Subgroups

6176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7545949);