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C₂×#60126 #10574121

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

Aliases

Subgroups

7602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,8)(6,7)(9,10)(11,12,15,19,16,20,26,32)(13,17,23,29,22,28,35,39)(14,18,25,31,24,30,36,40)(21,27,34,38,33,37,41,42);(4,7)(8,10)(11,13)(12,17)(14,21)(15,23)(16,22)(18,27)(19,29)(20,28)(24,33)(25,34)(26,35)(30,37)(31,38)(32,39)(36,41)(40,42);(3,5,6,9)(4,8,7,10)(11,14)(12,18)(13,21)(15,25)(16,24)(17,27)(19,31)(20,30)(22,33)(23,34)(26,36)(28,37)(29,38)(32,40)(35,41)(39,42);(14,24)(18,30)(21,33)(25,36)(27,37)(31,40)(34,41)(38,42);(13,22)(17,28)(21,33)(23,35)(27,37)(29,39)(34,41)(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, 10481317);