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C₂×#22206 #6376207

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

Aliases

Subgroups

2274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6283403);