#13180163

order	1728
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂	A₄⋊AGL(1,𝔽₉)
commutator, hypocenter	C₃²×SL(2,𝔽₃)	C₈
Fitting	C₃²×Q₈	C₃⋊C₈
socle	C₂×C₃²	A₄⋊C₈
prime radical	C₃⋊(C₃⋊(#41⋊C₃))	C₄
cosocle	#64289⋊C₃	C₂
LCS	G ▷ C₃²×SL(2,𝔽₃)
UCS	C₁ ◁ C₂

79 conjugacy classes of subgroups.

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 192

Polycyclic presentation:

2^3,3^3,2^3|a^2=b,b^2=c,c^2=i,g^2=i,h^2=i,d^a=d^2,e^a=e^2f^2,f^a=e^2,g^a=gh,h^a=hi,e^b=e^2f,f^b=ef,e^c=e^2,f^c=f^2,g^d=h,h^d=ghi,h^g=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46226);