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C₉⋊D₂₇ #92205

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

Aliases

Splittings

Subgroups

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 36 points:

(2,4)(3,7)(5,6)(8,9)(11,14)(12,18)(13,21)(15,16)(17,27)(19,20)(22,29)(23,28)(24,34)(25,33)(26,32)(30,31)(35,36);(1,9,4,7,6,5,3,2,8);(10,29,23,30,34,32,12,11,33,13,36,27,19,16,15,20,17,35,21,25,14,18,26,24,31,28,22)

Polycyclic presentation:

2,3^5|b^3=d^2f,c^3=e^2,d^3=f^2,b^a=b^2d,c^a=c^2e,d^a=d^2f,e^a=e^2,f^a=f^2

Conjugacy classes & character table

123 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 50);