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C₂×#33914 #7623798

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

Aliases

Subgroups

1352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 42 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530994);