#14312501

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂	#11748616
commutator, prime radical, cosocle	C₂⁴×C₃×C₅	C₂³
Frattini	C₂⁴	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×C₂²⋊C₄	C₂²
socle	C₂×C₃×C₅	#401
hypercenter	C₂×C₂²⋊C₄	D₃×D₅
hypocenter	C₃×C₅	#2104
LCS	G ▷ C₂⁴×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂×C₂²⋊C₄

356 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

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

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

Polycyclic presentation:

2^7,3,5|a^2=def,b^2=de,c^2=d,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,f^b=fg,i^b=i^4,e^c=eg,h^c=h^2,i^c=i^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38199);