AGL(1,𝔽₄₁) #13110011

order	1640
isoclinism	isoclinic class of AGL(1,𝔽₄₁)
automorphism	?
homology	Abelianization (H₁) = C₅×C₈ · Schur multiplier (H₂) = C₁

Aliases

affine general linear	AGL(1,𝔽₄₁)
unambiguous semidirect product	#66502⋊C₅

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₄₁	C₅×C₈
prime radical	D₄₁⋊C₅	C₄
cosocle	#4223	C₂×C₅
LCS	G ▷ C₄₁
UCS	C₁

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 41

Polycyclic presentation:

2,5,2^2,41|a^2=c,c^2=d,e^a=e^27,e^b=e^18,e^c=e^32,e^d=e^40

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1640, 47);