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C₂×#3223 #60795

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

Aliases

Subgroups

1011 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53783);