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C₂×#3209 #60778

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

Aliases

Subgroups

1067 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53766);