SL(2,ℤ/4)⋊#170 #14512424

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂²	AGL(1,𝔽₅)×S₄
commutator	C₂×C₅×A₄	C₂×C₈
Fitting, socle	C₂⁴×C₅	C₄×D₃
prime radical	C₂²×C₅×A₄	C₂×C₄
cosocle	C₂×A₄×Dic₅	C₂²
hypocenter	C₅×A₄	C₄⋊C₈
LCS	G ▷ C₂×C₅×A₄ ▷ C₅×A₄
UCS	C₁ ◁ C₂²

326 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 52 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 238122);