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C₂×#21296 #6372149

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

Aliases

Subgroups

2086 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)(11,12,16,20,17,21,15,30)(13,18,24,32,25,33,23,39)(14,26,29,34,27,40,28,19)(22,35,38,41,36,42,37,31);(4,7)(8,10)(11,13,16,24,17,25,15,23)(12,18,20,32,21,33,30,39)(14,22,29,38,27,36,28,37)(19,31,26,35,34,41,40,42);(11,14,15,28,17,27,16,29)(12,19,20,26,21,34,30,40)(13,22,23,37,25,36,24,38)(18,31,32,35,33,41,39,42);(3,5,6,9)(4,8,7,10)(14,27)(19,34)(22,36)(26,40)(28,29)(31,41)(35,42)(37,38)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279345);