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C₂×#10666 #243885

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

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, 151081);