#14514391

order	1920
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂	#11757174
commutator, hypocenter	C₅×C₂²⋊SL(2,𝔽₃)	C₄
Fitting	C₂²×C₅×Q₈	Dic₃
socle	C₂³×C₅	SL(2,ℤ/4)
prime radical, cosocle	D₅×C₂²⋊SL(2,𝔽₃)	C₂
LCS	G ▷ C₅×C₂²⋊SL(2,𝔽₃)
UCS	C₁ ◁ C₂

376 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.

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

μ_t(G) = 120

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240089);