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C₂×#60660 #10575271

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

Aliases

Subgroups

6474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482467);