D₂₁⋊AGL(1,𝔽₅) #11719847

order	840
isoclinism	isoclinic class of D₂₁⋊AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	D₂₁⋊AGL(1,𝔽₅)
unambiguous semidirect product	ΓL(1,𝔽₁₆)⋊D₇
unambiguous semidirect product	(C₇⋊AGL(1,𝔽₅))⋊D₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₇	C₂×C₄
prime radical	D₅×D₂₁	C₂
cosocle	C₃×C₇×D₅	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 105

Polycyclic presentation:

2^3,3,5,7|b^2=c,d^a=d^2,f^a=f^6,d^b=d^2,e^b=e^2,e^c=e^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(840, 149);