Finite Group Databasebeta

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C₃⋊#4208 #92401

• supersolvable
• solvable
• monomial

Aliases

Splittings

Subgroups

231 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 246);