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C₂×#61413 #10576702

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

Aliases

Subgroups

6850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 42 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483898);