AGL(1,𝔽₉)⋊C₁₆ #11772174

order	1152
isoclinism	isoclinic class of AΓL(1,𝔽₉)
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₈	AΓL(1,𝔽₉)
commutator	#157	C₂×C₁₆
Fitting	C₃²×C₈	SD₁₆
socle	C₂×C₃²	#334
prime radical	C₂×C₃⋊D₃	C₄⋊C₈
cosocle	C₈×#157	C₂²
hypocenter	C₃²	#1367
LCS	G ▷ #157 ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₈

90 conjugacy classes of subgroups.

μ_t(G) = 144

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 6185);