Finite Group Databasebeta

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D₁₀₃ #6086

• metacyclic
• supersolvable
• metabelian
• solvable
• monolithic
• monomial
• stem
• Frobenius
• ambivalent

Aliases

Splittings

Subgroups

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 103 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(2,103)(3,102)(4,101)(5,100)(6,99)(7,98)(8,97)(9,96)(10,95)(11,94)(12,93)(13,92)(14,91)(15,90)(16,89)(17,88)(18,87)(19,86)(20,85)(21,84)(22,83)(23,82)(24,81)(25,80)(26,79)(27,78)(28,77)(29,76)(30,75)(31,74)(32,73)(33,72)(34,71)(35,70)(36,69)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)

Polycyclic presentation:

2,103|b^a=b^102

Conjugacy classes & character table

53 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(206, 1);