Dic₃⋊GU(2,𝔽₃) #11920683

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₃×S₄
commutator	C₂×C₃×SL(2,𝔽₃)	C₂×C₄
Fitting	C₂×C₃×#41	C₂×D₃
socle	C₂²×C₃	C₂×SL(2,ℤ/4)
prime radical, cosocle	C₂×C₃×#41⋊C₃	C₂²
hypocenter	C₃×SL(2,𝔽₃)	C₄⋊C₄
LCS	G ▷ C₂×C₃×SL(2,𝔽₃) ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₄

307 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 307 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

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

μ_t(G) = 288

Polycyclic presentation:

2^4,3^2,2^3|a^2=d,b^2=c,c^2=i,g^2=i,h^2=i,b^a=bd,f^a=f^2,e^b=e^2,g^b=gh,h^b=hi,g^e=h,h^e=ghi,h^g=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154694);