#10605139⋊C₃ #14512092

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

Hall	#10605139 ⋊ C₃
Sylow	C₅ ⋊ #2645⋊C₃

	subgroup	G/H
center	C₂	C₂×C₅⋊(#126⋊C₃)
commutator, cosocle, hypocenter	C₅×#95	C₂²×C₃
Frattini	C₂³	C₂×D₅×A₄
Fitting	C₅×#376	C₂×C₃
socle	C₂³×C₅	C₂²×A₄
prime radical	C₅×#95⋊C₃	C₂²
hypercenter	C₄	C₅⋊(#126⋊C₃)
LCS	G ▷ C₅×#95
UCS	C₁ ◁ C₂ ◁ C₄

174 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.

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

μ_t(G) = 240

Polycyclic presentation:

2^2,3,2^2,5,2^3|a^2=gh,b^2=gh,d^2=g,e^2=gi,b^a=bgh,d^a=dhi,e^a=ei,f^a=f^4,d^c=de,e^c=dhi,g^c=ghi,h^c=i,i^c=hi,e^d=egh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237790);