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C₂×#1858 #20859

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

Aliases

Subgroups

655 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,8,12,9,13,7,20)(5,14,16,10,17,25,21,24)(6,11,18,27,19,28,22,26)(15,30,33,34,32,29,31,23);(3,5,8,16,9,17,7,21)(4,10,12,25,13,24,20,14)(6,15,18,33,19,32,22,31)(11,23,27,30,28,34,26,29);(3,6)(4,11)(5,15)(7,22)(8,18)(9,19)(10,23)(12,27)(13,28)(14,29)(16,33)(17,32)(20,26)(21,31)(24,34)(25,30)

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, 13847);