A₄⋊#672 #11746599

order	960
isoclinism	isoclinic class of C₅⋊S₄
automorphism	?
homology	Abelianization (H₁) = C₁₆ · Schur multiplier (H₂) = C₂

Aliases

derived	C₅×A₄ ⋊ C₁₆
Sylow	C₅ ⋊ A₄⋊C₁₆

	subgroup	G/H
center, Frattini, hypercenter	C₈	C₅⋊S₄
commutator, hypocenter	C₅×A₄	C₁₆
Fitting	C₂²×C₅×C₈	D₃
socle	C₂³×C₅	C₃⋊C₈
prime radical	C₂×C₅×A₄	C₈
cosocle	C₅×C₈×A₄	C₂
LCS	G ▷ C₅×A₄
UCS	C₁ ◁ C₈

66 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 240

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 794);