C₅⋊AGL(1,𝔽₁₉) #13133755

order	1710
isoclinism	isoclinic class of C₅⋊AGL(1,𝔽₁₉)
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₅⋊AGL(1,𝔽₁₉)
unambiguous semidirect product	#4296⋊D₅

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉	C₂×C₉
prime radical	C₅⋊(D₁₉⋊C₃)	C₃
cosocle	C₅×C₁₉⋊C₃	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 95

Polycyclic presentation:

2,3^2,5,19|b^3=c,d^a=d^4,e^a=e^18,e^b=e^4,e^c=e^7

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1710, 15);