C₅⋊#67992 #14511526

order	1920
isoclinism	isoclinic class of C₅⋊#67992
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅×C₈²⋊C₃	C₂
Frattini	C₄²	C₅⋊S₄
Fitting	C₅×C₈²	D₃
socle	C₂²×C₅	#857
LCS	G ▷ C₅×C₈²⋊C₃
UCS	C₁

94 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 120

Polycyclic presentation:

2,3,5,2^6|d^2=f,e^2=g,f^2=h,g^2=i,b^a=b^2,c^a=c^4,d^a=deghi,e^a=eg,f^a=fgi,g^a=gi,h^a=hi,d^b=efhi,e^b=de,f^b=gh,g^b=fg,h^b=i,i^b=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237224);