C₃⋊#91184 #13086218

order	1440
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃

Aliases

derived	C₃×C₅×SL(2,𝔽₃) ⋊ C₄
Sylow	C₅ ⋊ C₃⋊#859

	subgroup	G/H
center, Frattini, hypercenter	C₂²	C₃⋊(C₅⋊S₄)
commutator, hypocenter	C₃×C₅×SL(2,𝔽₃)	C₄
Fitting	C₂×C₃×C₅×Q₈	D₃
socle	C₂²×C₃×C₅	S₄
prime radical, cosocle	C₂×C₃×C₅×SL(2,𝔽₃)	C₂
LCS	G ▷ C₃×C₅×SL(2,𝔽₃)
UCS	C₁ ◁ C₂²

156 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

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

μ_t(G) = 480

Polycyclic presentation:

2^2,3^2,5,2^3|a^2=b,f^2=h,g^2=h,c^a=c^2,d^a=d^2,e^a=e^4,f^a=fg,g^a=gh,f^c=g,g^c=fgh,g^f=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 2535);