#10624536⋊C₂ #13090587

order	1458
isoclinism	isoclinic class of #10624536⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#10624536	C₂
Frattini	C₉²	C₃⋊D₃
socle	C₃	#92216
LCS	G ▷ #10624536
UCS	C₁

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 81

Polycyclic presentation:

2,3^6|b^3=g,c^3=e^2f,d^3=f^2g,e^3=g^2,b^a=b^2de^2f^2,c^a=c^2ef^2g,d^a=de^2f,e^a=e^2f^2g,g^a=g^2,c^b=cd,d^b=de,e^b=ef,f^b=fg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 661);