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C₂×#60315 #10574475

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

Aliases

Subgroups

6602 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)(11,12,15,20,16,18,27,31)(13,17,23,30,21,28,35,39)(14,24,25,38,26,19,32,33)(22,36,37,42,34,29,40,41);(3,5)(4,7)(6,10)(8,9)(11,13)(12,17)(14,22)(15,23)(16,21)(18,28)(19,29)(20,30)(24,36)(25,37)(26,34)(27,35)(31,39)(32,40)(33,41)(38,42);(5,10)(7,9)(12,18)(13,21)(19,24)(20,31)(22,34)(23,35)(33,38)(37,40);(4,8)(7,9)(13,21)(17,28)(22,34)(23,35)(29,36)(30,39)(37,40)(41,42);(11,14,15,25,16,26,27,32)(12,19,20,33,18,24,31,38)(13,22,23,37,21,34,35,40)(17,29,30,41,28,36,39,42)

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, 10481671);