C₅⋊#6057 #11758797

order	1000
isoclinism	isoclinic class of C₅⋊#6057
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₅

Aliases

C₅³ ⋊ Q₈

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, prime radical, cosocle	C₅×C₅⋊D₅	C₂²
Fitting, socle, hypocenter	C₅³	Q₈
LCS	G ▷ C₅×C₅⋊D₅ ▷ C₅³
UCS	C₁

48 conjugacy classes of subgroups.

μ_t(G) = 40

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1000, 182);