#11790081

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

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₃²
commutator, socle, prime radical	C₂³×C₃²	C₂²×C₄
Fitting	C₂²×C₃²×C₈	C₂²
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	#1940
LCS	G ▷ C₂³×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

569 conjugacy classes of subgroups.

μ_t(G) = 384

Polycyclic presentation:

2^7,3^2|a^2=f,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=ce,i^a=hi^2,c^b=cg,h^b=h^2,i^b=i^2,h^c=h^2,i^c=i^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 24092);