#11920668

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

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂³	D₃×S₄
commutator	C₂×C₃×SL(2,𝔽₃)	C₂×C₄
Fitting	C₂²×C₃×Q₈	C₂×D₃
socle	C₂³×C₃	C₂×S₄
prime radical, cosocle	C₂²×C₃×SL(2,𝔽₃)	C₂²
hypocenter	C₃×SL(2,𝔽₃)	C₄⋊C₄
LCS	G ▷ C₂×C₃×SL(2,𝔽₃) ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂³

375 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 375 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

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

μ_t(G) = 384

Polycyclic presentation:

2^4,3^2,2^3|a^2=d,b^2=c,g^2=i,h^2=i,b^a=bc,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, 154679);