A₄⋊Dic₁₇ #11717833

order	816
isoclinism	isoclinic class of A₄⋊D₁₇
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₂

Aliases

A₄⋊Dic₁₇

derived	A₄×C₁₇ ⋊ C₄
Sylow	C₁₇ ⋊ SL(2,ℤ/4)

	subgroup	G/H
center, Frattini, hypercenter	C₂	A₄⋊D₁₇
commutator, hypocenter	A₄×C₁₇	C₄
Fitting, socle	C₂³×C₁₇	D₃
prime radical, cosocle	C₂×A₄×C₁₇	C₂
LCS	G ▷ A₄×C₁₇
UCS	C₁ ◁ C₂

38 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 204

Polycyclic presentation:

2^2,3,17,2^2|a^2=b,c^a=c^2,d^a=d^16,e^a=f,f^a=e,e^c=f,f^c=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(816, 103);