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C₃⋊#4185 #92342

• supersolvable
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

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, 187);