Dic₃⋊#1088 #13048231

order	1296
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₃×#157
commutator, Fitting	C₂×C₃×H(3,𝔽₃)	C₂×C₄
socle	C₂×C₃²	C₂×#157
prime radical, cosocle	C₂×C₃×#272	C₂²
hypocenter	C₃×H(3,𝔽₃)	C₄⋊C₄
LCS	G ▷ C₂×C₃×H(3,𝔽₃) ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃

178 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.

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

μ_t(G) = 72

Polycyclic presentation:

2^4,3^4|a^2=d,b^2=c,b^a=bd,g^a=g^2,e^b=ef,f^b=ef^2h^2,e^c=e^2,f^c=f^2h,f^e=fh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1949);