#13158798

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

No aliases for this group.

C₃³ ⋊ #446

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₃×C₃⋊D₃
commutator, socle, prime radical	C₂²×C₃³	C₂²×C₄
Fitting	C₃³×C₄²	C₂²
cosocle	C₂×C₃³×C₄	C₂³
hypercenter	C₄²	D₃×C₃⋊D₃
hypocenter	C₃³	#446
LCS	G ▷ C₂²×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

844 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.

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

μ_t(G) = 576

Polycyclic presentation:

2^6,3^3|a^2=e,b^2=d,c^2=def,d^2=f,e^2=f,b^a=bf,g^a=g^2,h^a=h^2,c^b=cdef,i^b=i^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 24861);