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C₂×#3327 #61147

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

Aliases

Subgroups

1057 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 54135);