C₄⋊(C₅⋊#226) #11752109

order	960
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini	C₂²	C₂×C₅⋊S₄
commutator, prime radical, cosocle	C₂×C₅×SL(2,𝔽₃)	C₂²
Fitting	C₄×C₅×Q₈	D₃
socle	C₂²×C₅	C₂×S₄
hypercenter	C₂×C₄	C₅⋊S₄
hypocenter	C₅×SL(2,𝔽₃)	D₄
LCS	G ▷ C₂×C₅×SL(2,𝔽₃) ▷ C₅×SL(2,𝔽₃)
UCS	C₁ ◁ C₂² ◁ C₂×C₄

134 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.

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

μ_t(G) = 320

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 6304);