#11794305

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

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	#64091
commutator, prime radical, cosocle	C₂⁴×C₃²	C₂³
Frattini	C₂⁴	C₂²×C₃⋊D₃
Fitting	C₃²×#342	C₂
socle	C₂²×C₃²	#120
hypercenter	#342	C₃⋊D₃
hypocenter	C₃²	#2062
LCS	G ▷ C₂⁴×C₃² ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #342

942 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.

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

μ_t(G) = 288

Polycyclic presentation:

2^7,3^2|a^2=d,b^2=d,c^2=d,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,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, 28316);