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C₂×#3374 #61309

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

Aliases

Subgroups

889 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54297);