#14511801

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂³	D₅×S₄
commutator	C₂×C₅×SL(2,𝔽₃)	C₂×C₄
Fitting	C₂²×C₅×Q₈	C₂×D₃
socle	C₂³×C₅	C₂×S₄
prime radical, cosocle	C₂²×C₅×SL(2,𝔽₃)	C₂²
hypocenter	C₅×SL(2,𝔽₃)	C₄⋊C₄
LCS	G ▷ C₂×C₅×SL(2,𝔽₃) ▷ C₅×SL(2,𝔽₃)
UCS	C₁ ◁ C₂³

318 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 640

Polycyclic presentation:

2^4,3,5,2^3|a^2=d,b^2=c,g^2=i,h^2=i,b^a=bdi,f^a=f^4,e^b=e^2,g^b=gh,h^b=hi,g^e=h,h^e=ghi,h^g=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237499);