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C₂×#63063 #10586382

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

Aliases

Subgroups

33844 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10493578);