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C₂×#2596 #34853

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

Aliases

Subgroups

1037 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 27841);