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C₂×#33747 #7623242

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

Aliases

Subgroups

1418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530438);