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C₂×#62871 #10586204

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

Aliases

Subgroups

33898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 42 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493400);