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D₁₆₅₃ #15693255

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

Aliases

Splittings

Subgroups

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 51 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);(2,3)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(24,51)(25,50)(26,49)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)

Polycyclic presentation:

2,3,19,29|b^a=b^2,c^a=c^18,d^a=d^28

Conjugacy classes & character table

828 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3306, 9);