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C₂×#10667 #243886

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

Aliases

Subgroups

876 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 151082);