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C₂×#2769 #52208

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

Aliases

Subgroups

883 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,7,5)(6,9,10,8)(11,12)(13,16)(14,15)(17,18)(21,24)(22,26);(4,5)(6,10)(12,14)(16,17)(19,20,23,25)(21,22,24,26);(3,5,7,4)(6,9,10,8)(11,13,15,18)(12,16,14,17)(19,21,23,24)(20,22,25,26);(3,6,7,10)(4,8,5,9)(11,14,15,12)(13,17,18,16)(19,22)(20,24)(21,25)(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, 45196);