D₅⋊#1043 #11758783

order	1000
isoclinism	isoclinic class of D₅⋊#1043
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	D₅⋊#1043
unambiguous semidirect product	#92562⋊C₂

C₅³ ⋊ C₂×C₄

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅³	C₂×C₄
prime radical	D₅×C₅⋊D₅	C₂
cosocle	C₅⋊(C₅⋊D₅)	C₂²
LCS	G ▷ C₅³
UCS	C₁

200 conjugacy classes of subgroups.

μ_t(G) = 50

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1000, 168);