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C₂×#60191 #10574216

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

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, 10481412);