#14299045

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂³	C₂²×ΓL(1,𝔽₁₆)
commutator, socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
Fitting	C₃×C₅×#95	C₄
cosocle	C₂²×C₃×Dic₅	C₂³
hypercenter	#95	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	#1843
LCS	G ▷ C₂³×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ #95

512 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 193 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=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^2,i^a=i^2,c^b=cg,i^f=i^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24743);