(C₂×AGL(1,𝔽₅))⋊(C₃⋊C₁₆) #14278693

order	1920
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₆ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
commutator	C₂×C₃×C₅	C₄×C₁₆
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂²×C₃×C₅	C₄×C₈
prime radical	C₂²×C₃×D₅	C₂×C₈
cosocle	C₂×C₃×C₈×D₅	C₂²
hypocenter	C₃×C₅	#1374
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈

320 conjugacy classes of subgroups.

μ_t(G) = 480

Polycyclic presentation:

2^7,3,5|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,h^a=h^2,i^b=i^2,i^e=i^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4391);