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C₂×#33678 #7623085

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

Aliases

Subgroups

1622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530281);