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C₂×#33475 #7622641

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

Aliases

Subgroups

1354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529837);