#11920936

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₃

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂	C₂×C₃⋊#857
commutator, prime radical, cosocle	C₂×C₃×C₄²⋊C₃	C₂²
Frattini	C₂³	C₂×C₃⋊S₄
Fitting	C₃×C₄³	D₃
socle	C₂³×C₃	C₂×S₄
hypercenter	C₄	C₃⋊#857
hypocenter	C₃×C₄²⋊C₃	Q₈
LCS	G ▷ C₂×C₃×C₄²⋊C₃ ▷ C₃×C₄²⋊C₃
UCS	C₁ ◁ C₂ ◁ C₄

276 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 33 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:

2^3,3^2,2^4|a^2=c,b^2=c,f^2=h,g^2=i,b^a=bc,d^a=d^2,e^a=e^2,f^a=fg,g^a=gi,h^a=hi,f^d=ghi,g^d=fgh,h^d=i,i^d=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154947);