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C₂×#1922 #21040

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

Aliases

Subgroups

427 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 14028);