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C₂×C₃⋊C₆₄ #67586

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 69 points:

(1,2)(4,5)(6,7,8,13,9,14,18,28,10,15,19,29,22,32,38,48,11,16,20,30,23,33,39,49,25,35,41,51,44,54,58,63,12,17,21,31,24,34,40,50,26,36,42,52,45,55,59,64,27,37,43,53,46,56,60,65,47,57,61,66,62,67,68,69);(1,2)(3,4,5)

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 162);