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C₂×#12884 #494071

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

Aliases

Subgroups

722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 42 points:

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

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, 401267);