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C₂×#60307 #10574467

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

Aliases

Subgroups

6618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 42 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481663);