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C₂×#10670 #243889

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

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, 151085);