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C₃⋊#1035 #64463

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 28 points:

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

Polycyclic presentation:

2^2,3,5^2|a^2=b,d^5=e^2,c^a=c^2,d^a=d^3e,e^a=e^3,d^b=d^4e^3,e^b=e^4

Conjugacy classes & character table

24 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 6);