C₃⋊#68002 #11920138

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

Aliases

	subgroup	G/H
center, hypercenter	C₂	C₃⋊#4625
commutator, prime radical, hypocenter	C₃×C₂²⋊SL(2,𝔽₃)	C₄
Frattini	C₂²×C₄	C₃⋊S₄
Fitting	C₃×#395	D₃
socle	C₂³×C₃	SL(2,ℤ/4)
cosocle	C₃×#395⋊C₃	C₂
LCS	G ▷ C₃×C₂²⋊SL(2,𝔽₃)
UCS	C₁ ◁ C₂

134 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 23 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:

2^2,3^2,2^5|a^2=b,b^2=i,e^2=i,f^2=i,c^a=c^2,d^a=d^2,e^a=efg,f^a=fghi,g^a=gh,e^b=eg,f^b=fh,e^c=f,f^c=efi,g^c=h,h^c=gh,f^e=fi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154149);