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C₂×#3177 #60681

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

Aliases

Subgroups

921 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 42 points:

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

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, 53669);