A₄⋊Dic₁₉ #11744908

order	912
isoclinism	isoclinic class of A₄⋊D₁₉
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	A₄⋊Dic₁₉
unambiguous semidirect product	C₁₉⋊SL(2,ℤ/4)

derived	A₄×C₁₉ ⋊ C₄
Sylow	C₁₉ ⋊ SL(2,ℤ/4)

	subgroup	G/H
center, Frattini, hypercenter	C₂	A₄⋊D₁₉
commutator, hypocenter	A₄×C₁₉	C₄
Fitting, socle	C₂³×C₁₉	D₃
prime radical, cosocle	C₂×A₄×C₁₉	C₂
LCS	G ▷ A₄×C₁₉
UCS	C₁ ◁ C₂

38 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 228

Polycyclic presentation:

2^2,3,19,2^2|a^2=b,c^a=c^2,d^a=d^18,e^a=f,f^a=e,e^c=f,f^c=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(912, 119);