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C₂×#2245 #33700

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

Aliases

Subgroups

291 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 42 points:

(1,2);(3,4)(5,8)(6,7)(9,10)(11,12,18,24)(13,20,28,39)(14,19,30,37)(15,22,32,34)(16,21,25,40)(17,33,31,23)(26,38,41,36)(27,42,29,35);(4,7)(8,10)(11,13,25,41,17,27,15,14,18,28,16,26,31,29,32,30)(12,19,34,42,23,36,21,20,24,37,22,35,33,38,40,39);(3,5,6,9)(4,8,7,10)(11,14,15,29,31,41,25,28,18,30,32,27,17,26,16,13)(12,20,21,38,33,42,34,37,24,39,40,36,23,35,22,19)

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 26688);