#11923773

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂³×C₃

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂	C₂×C₃⋊#1020
commutator, cosocle, hypocenter	C₃×C₂²⋊SL(2,𝔽₃)	C₂²
Fitting	C₂²×C₃×#41	D₃
socle	C₂³×C₃	C₂×S₄
prime radical	C₃×#5948	C₂
hypercenter	C₄	C₃⋊#1020
LCS	G ▷ C₃×C₂²⋊SL(2,𝔽₃)
UCS	C₁ ◁ C₂ ◁ C₄

584 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 35 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:

2^2,3^2,2^5|a^2=i,b^2=i,g^2=i,h^2=i,b^a=bi,c^a=c^2,d^a=d^2,e^a=ef,g^a=gh,h^a=hi,e^c=f,f^c=ef,g^c=h,h^c=ghi,h^g=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 157784);