Finite Group Databasebeta

?

← Prev (#10576705) Next (#10576707) →

C₂×#61416 #10576706

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

Aliases

Subgroups

6742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483902);