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C₃⋊Dic₂₇ #66329

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

42 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 34 points:

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

Polycyclic presentation:

2^2,3^4|a^2=b,c^3=e^2f,e^3=f^2,c^a=c^2e,d^a=d^2,e^a=e^2f,f^a=f^2

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 21);