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C₂×C₇₃⋊C₃ #89142

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(438, 2);