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C₂×C₇₉⋊C₃ #90902

• 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 81 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)(27,39,52)(30,42,50)(33,45,47)(36,48,44)(38,40,41)(43,55,65)(46,58,63)(49,61,60)(51,56,57)(53,66,54)(59,67,74)(62,70,72)(64,68,69)(71,75,79)(73,76,77)(78,80,81);(3,4,6,10,17,27,40,24,34,47,60,69,55,26,38,51,64,73,78,80,70,45,19,5,8,13,20,30,43,56,35,14,21,31,44,57,39,53,52,65,74,79,81,75,58,29,9,15,23,33,46,59,68,48,22,7,11,18,28,41,54,66,37,50,63,72,77,67,42,16,25,36,49,62,71,76,61,32,12)

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(474, 2);