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C₂×#33943 #7623872

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

Aliases

Subgroups

1334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 42 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531068);