#13163618

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²×C₃³

Aliases

No aliases for this group.

C₃³ ⋊ #398

	subgroup	G/H
center, Frattini	C₂³	C₂²×C₃⋊(C₃⋊D₃)
commutator, socle, prime radical, cosocle	C₂³×C₃³	C₂³
Fitting	C₂×C₃³×C₄⋊C₄	C₂
hypercenter	C₂×C₄⋊C₄	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	#398
LCS	G ▷ C₂³×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

2100 conjugacy classes of subgroups; only the 633 normal subgroups are shown.

normal subgroups only

This group has 2100 conjugacy classes of subgroups — too many to draw. Only its 633 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 1728

Polycyclic presentation:

2^6,3^3|a^2=f,b^2=f,c^2=f,b^a=be,c^a=cef,g^a=g^2,h^a=h^2,i^a=i^2,c^b=cd

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 29681);