#41013552

order	27008
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₂₁₁ ⋊ #1843

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₁₁
commutator, socle, prime radical	C₂³×C₂₁₁	C₂²×C₄
Fitting	#376×C₂₁₁	C₂
cosocle	C₂²×C₄×C₂₁₁	C₂³
hypercenter	#376	D₂₁₁
hypocenter	C₂₁₁	#1843
LCS	G ▷ C₂³×C₂₁₁ ▷ C₂₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ #376

256 conjugacy classes of subgroups.

μ_t(G) = 27008

Polycyclic presentation:

2^7,211|a^2=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^210,c^b=cg

4244 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27008, 4664);