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C₂×#2810 #52271

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

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, 45259);