#10624577⋊C₂ #13090682

order	1458
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₃	#92314
commutator, cosocle, hypocenter	#6855	C₂×C₃
Frattini, socle	C₃³	C₃×C₃⋊D₃
Fitting	#10624577	C₂
prime radical	#92197	C₃
LCS	G ▷ #6855
UCS	C₁ ◁ C₃

176 conjugacy classes of subgroups.

μ_t(G) = 162

Polycyclic presentation:

2,3^6|b^3=efg,c^3=ef^2,d^3=e,b^a=bcdeg^2,c^a=b^2de^2f^2,d^a=bc^2df^2g^2,e^a=ef^2g,f^a=eg^2,g^a=efg,c^b=ce,d^b=df,d^c=dg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 756);