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C₂×#13456 #499201

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

Aliases

Subgroups

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406397);