#11808946

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²×C₄	C₂²×D₉
commutator, cosocle	C₂³×C₉	C₂⁴
Frattini, socle, prime radical	C₂³×C₃	C₂³×D₃
Fitting	C₄×C₉×C₄⋊C₄	C₂
hypercenter	C₄×C₄⋊C₄	D₉
hypocenter	C₉	#2402
LCS	G ▷ C₂³×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

600 conjugacy classes of subgroups.

μ_t(G) = 1152

Polycyclic presentation:

2^7,3^2|a^2=g,b^2=f,c^2=f,d^2=e,h^3=i,b^a=be,c^a=cf,h^a=h^2i^2,i^a=i^2,c^b=cg,h^b=h^2i^2,i^b=i^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 42957);