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C₂×#13640 #512726

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

Aliases

Subgroups

442 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)(11,12,13,18,14,19,21,30,15,20,22,31,24,32,33,40,16,17,23,27,25,28,34,37,26,29,35,38,36,39,41,42);(4,7)(8,10);(3,5,6,9)(4,8,7,10)(12,17)(18,27)(19,28)(20,29)(30,37)(31,38)(32,39)(40,42)

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 419922);