#84124⋊C₃ #11921382

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center	C₂	C₂×C₃⋊(#120⋊C₃)
commutator, cosocle, hypocenter	C₃×H(5,𝔽₂)	C₂²×C₃
Frattini	C₂³	C₂×D₃×A₄
Fitting	C₃×#585	C₂×C₃
socle	C₂×C₃	C₂×#120⋊C₃
prime radical	C₃×#5950	C₂
hypercenter	C₄	C₃⋊(#120⋊C₃)
LCS	G ▷ C₃×H(5,𝔽₂)
UCS	C₁ ◁ C₂ ◁ C₄

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

normal subgroups only

This group has 330 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) = 96

Polycyclic presentation:

2^2,3,2^4,3,2|a^2=i,b^2=i,b^a=bi,d^a=df,e^a=efg,h^a=h^2,d^c=de,e^c=d,f^c=gi,g^c=fgi,g^d=gi,f^e=fi,g^e=gi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 155393);