C₃⋊#73166 #11921132

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₄

Aliases

unambiguous semidirect product	C₃⋊#73166
unambiguous semidirect product	#73383⋊C₃

	subgroup	G/H
center	C₂	C₂×D₃×C₄²⋊C₃
commutator, cosocle, hypocenter	C₃×#95	C₂²×C₃
Frattini	C₂³	C₂×D₃×A₄
Fitting	C₃×#376	C₂×C₃
socle	C₂³×C₃	C₂²×A₄
prime radical	C₃×#95⋊C₃	C₂²
hypercenter	C₄	D₃×C₄²⋊C₃
LCS	G ▷ C₃×#95
UCS	C₁ ◁ C₂ ◁ C₄

274 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.

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

μ_t(G) = 144

Polycyclic presentation:

2^2,3,2^2,3,2^3|a^2=gh,b^2=gh,d^2=g,e^2=gi,b^a=bgh,f^a=f^2,d^c=de,e^c=dhi,g^c=ghi,h^c=i,i^c=hi,e^d=egh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 155143);