Finite Group Databasebeta

?

← Prev (#92428) Next (#92430) →

C₂×#6923 #92429

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 63 points:

(4,5,6,8)(7,10,11,17)(9,14,15,13)(12,19,20,30)(16,23,24,26)(18,27,28,22)(21,32,33,47)(25,36,37,43)(29,40,41,39)(31,44,45,35)(34,49,50,51)(38,53,54,62)(42,57,58,60)(46,61,59,56)(48,63,55,52);(1,2)(3,4,7,12,21,34,51,63,44,27,14,5,9,16,25,38,55,47,62,61,40,23,10,18,29,42,59,45,30,43,60,57,36,19,31,46,58,41,28,17,26,39,56,53,32,48,54,37,24,15,8,13,22,35,52,49,50,33,20,11,6)

Conjugacy classes & character table

38 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(488, 12);