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C₂×C₆₇⋊C₃ #87930

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(402, 2);