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C₂×#62887 #10586222

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

Aliases

Subgroups

33822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10493418);