C₃⋊(C₃⋊Dic₉) #66411

order	324
isoclinism	isoclinic class of C₃⋊(C₃⋊D₉)
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃³

Aliases

unambiguous semidirect product	C₃⋊(C₃⋊Dic₉)
unambiguous semidirect product	C₉⋊(C₃⋊Dic₃)

C₃²×C₉ ⋊ C₄

150 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 324

A minimal faithful permutation representation — 4 generators on 19 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 103);