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C₂×#2514 #34779

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

Aliases

Subgroups

971 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27767);