#13099804

order	1600
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₅² ⋊ #346

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₅×AGL(1,𝔽₅)
commutator	C₂×C₅²	C₄×C₈
Fitting	C₂×C₄×C₅²	C₂×C₄
socle, prime radical	C₂²×C₅²	C₂×C₈
cosocle	C₂×C₅×#168	C₂²
hypocenter	C₅²	#346
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₄

119 conjugacy classes of subgroups.

μ_t(G) = 320

Polycyclic presentation:

2^6,5^2|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bf,h^a=h^4,g^b=g^2,g^c=g^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 2156);