#14512374

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

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂²	AGL(1,𝔽₅)×S₄
commutator	C₂×C₅×SL(2,𝔽₃)	C₂×C₄
Fitting	C₂×C₅×Q₈	C₄×D₃
socle	C₂²×C₅	C₄×S₄
prime radical, cosocle	C₂×C₅⋊(#41⋊C₃)	C₂²
hypocenter	C₅×SL(2,𝔽₃)	C₄⋊C₄
LCS	G ▷ C₂×C₅×SL(2,𝔽₃) ▷ C₅×SL(2,𝔽₃)
UCS	C₁ ◁ C₂²

258 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.

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

μ_t(G) = 480

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 238072);