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C₂×#2791 #52235

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

Aliases

Subgroups

927 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)(13,17)(14,15)(16,18)(19,20,23,26)(21,25,22,24);(4,7)(8,10)(11,13,15,18)(12,16,14,17);(3,4,6,7)(5,8,9,10)(11,14,15,12)(13,16,18,17)(19,21,23,22)(20,24,26,25);(3,5,6,9)(4,8,7,10)(11,13)(12,17)(14,16)(15,18)(19,22,23,21)(20,25,26,24)

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, 45223);