Finite Group Databasebeta

?

← Prev (#10620585) Next (#10620587) →

C₃×#6403 #10620586

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 42 points:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 168);