D₅⋊#1035 #11758705

order	1000
isoclinism	isoclinic class of D₅⋊#1035
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	D₅⋊#1035
unambiguous semidirect product	D₂₅⋊AGL(1,𝔽₅)
unambiguous semidirect product	#92536⋊C₂
unambiguous semidirect product	#92538⋊C₂

C₅×C₂₅ ⋊ C₂×C₄

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₂₅	C₂×C₄
Frattini	C₅	D₅⋊AGL(1,𝔽₅)
socle	C₅²	C₂×AGL(1,𝔽₅)
prime radical	D₅×D₂₅	C₂
cosocle	C₅⋊D₂₅	C₂²
LCS	G ▷ C₅×C₂₅
UCS	C₁

60 conjugacy classes of subgroups.

μ_t(G) = 50

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1000, 90);