#14277481

order	1920
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₆ · Schur multiplier (H₂) = C₄

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₄²	D₃×AGL(1,𝔽₅)
commutator	C₂×C₃×C₅	C₄×C₁₆
Fitting	C₃×C₄²×C₅	C₂×C₄
socle, prime radical	C₂²×C₃×C₅	C₄×C₈
cosocle	C₃×C₄×#168	C₂²
hypocenter	C₃×C₅	#1312
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄²

184 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

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

μ_t(G) = 1920

Polycyclic presentation:

2^7,3,5|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,b^a=be,h^a=h^2,i^b=i^2,i^d=i^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 3179);