Finite Group Databasebeta

?

← Prev (#67265) Next (#67267) →

C₂×C₂₃⋊C₈ #67266

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

22 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 33 points:

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

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(368, 8);