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C₃⋊((C₂²⋊C₉)⋊C₄) #88612

• solvable
• monomial

Aliases

Splittings

Subgroups

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 20 points:

(1,2,3,4)(5,6,8,7)(10,11)(13,15)(14,18)(16,17)(19,20);(9,10,11);(6,7,8)(12,20,15,18,17,16,14,13,19)

Polycyclic presentation:

2^2,3^3,2^2|a^2=b,c^3=e^2,c^a=c^2e,d^a=d^2,e^a=e^2,f^a=g,g^a=f,f^c=g,g^c=fg

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 259);