#14511624

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

Aliases

No aliases for this group.

	subgroup	G/H
center, hypercenter	C₂	D₅×#857
commutator, prime radical, cosocle	C₂×C₅×C₄²⋊C₃	C₂²
Frattini	C₂³	D₅×S₄
Fitting	C₂×C₄²×C₅	C₂×D₃
socle	C₂³×C₅	C₂×S₄
hypocenter	C₅×C₄²⋊C₃	Q₈
LCS	G ▷ C₂×C₅×C₄²⋊C₃ ▷ C₅×C₄²⋊C₃
UCS	C₁ ◁ C₂

240 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 24 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:

2^3,3,5,2^4|a^2=c,b^2=c,f^2=h,g^2=i,b^a=bc,e^a=e^4,d^b=d^2,f^b=fgi,g^b=gi,h^b=hi,f^d=gh,g^d=fg,h^d=i,i^d=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237322);