#14511682

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₅×S₄
commutator, hypocenter	C₅×SL(2,𝔽₃)	C₂×C₈
Fitting	C₄×C₅×Q₈	C₂×D₃
socle	C₂²×C₅	C₂×SL(2,ℤ/4)
prime radical	C₂×D₅×SL(2,𝔽₃)	C₄
cosocle	C₄×C₅×SL(2,𝔽₃)	C₂²
LCS	G ▷ C₅×SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₄

244 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.

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

μ_t(G) = 320

Polycyclic presentation:

2^4,3,5,2^3|b^2=c,c^2=d,g^2=i,h^2=i,b^a=bi,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, 237380);