#11805590

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂³	C₂³×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini, socle, prime radical	C₂³×C₃	C₂³×D₃
Fitting	C₄×C₉×C₄⋊C₄	C₂
cosocle	C₂³×C₉	C₂⁴
hypercenter	C₄×C₄⋊C₄	D₉
hypocenter	C₉	#2351
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄

828 conjugacy classes of subgroups.

μ_t(G) = 1152

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 39601);