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C₂×#3356 #61249

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

Aliases

Subgroups

933 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)(11,12,14,18)(13,20,21,16)(15,17,23,19)(22,24,26,25);(3,5)(4,8)(6,9)(7,10)(11,13,14,21)(12,16,18,20)(15,22,23,26)(17,25,19,24);(3,6,7,4)(5,9,10,8)(12,17)(13,21)(15,23)(16,24)(18,19)(20,25);(5,10)(8,9)(12,18)(13,21)(17,19)(22,26)

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54237);