#10620192⋊C₃ #14517904

order	1944
isoclinism	isoclinic class of #10620192⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₈ · Schur multiplier (H₂) = C₁

Aliases

Fitting, Sylow	C₃²⋊H(3,𝔽₃) ⋊ C₈
derived	C₃⁴ ⋊ C₃×C₈

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 27

Polycyclic presentation:

2,3,2^2,3^4|a^2=c,c^2=d,e^a=e^2f^2,f^a=e^2,g^a=gh,h^a=g^2h,e^b=eg^2,f^b=fg^2h,e^c=e^2f,f^c=ef,g^c=h^2,h^c=g,e^d=e^2,f^d=f^2,g^d=g^2,h^d=h^2

maximal subgroup of	#72221986, #72222001, #72222004
maximal normal subgroup of	#72221986, #72222001, #72222004

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2298);