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C₃⋊#4207 #92400

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

225 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 245);