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C₂×#2762 #52200

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

Aliases

Subgroups

915 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45188);