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C₃⋊#4184 #92341

• supersolvable
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 30 points:

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

Polycyclic presentation:

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

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 186);