#14522147

order	2000
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, hypercenter	C₂²	((C₅⋊D₅)⋊C₅)⋊C₂
commutator	C₂×H(3,𝔽₅)	C₂×C₄
Frattini, socle	C₂²×C₅	D₅²
Fitting, prime radical, cosocle	C₂²×H(3,𝔽₅)	C₂²
hypocenter	H(3,𝔽₅)	C₄⋊C₄
LCS	G ▷ C₂×H(3,𝔽₅) ▷ H(3,𝔽₅)
UCS	C₁ ◁ C₂²

123 conjugacy classes of subgroups.

μ_t(G) = 400

Polycyclic presentation:

2^4,5^3|a^2=d,b^2=c,b^a=bd,f^a=f^4,g^a=g^4,e^b=e^4,g^b=g^4,f^e=fg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 110);