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C₂×#10668 #243887

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

Aliases

Subgroups

762 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 151083);