Dic₁₂₁⋊C₄ #14515417

order	1936
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

Dic₁₂₁⋊C₄

C₁₂₁ ⋊ C₄⋊C₄

	subgroup	G/H
center	C₂²	C₂×D₁₂₁
commutator	C₂×C₁₂₁	C₂×C₄
Frattini, socle, prime radical	C₂²×C₁₁	C₂×D₁₁
Fitting	C₂×C₄×C₁₂₁	C₂
cosocle	C₂²×C₁₂₁	C₂²
hypercenter	C₂×C₄	D₁₂₁
hypocenter	C₁₂₁	C₄⋊C₄
LCS	G ▷ C₂×C₁₂₁ ▷ C₁₂₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄

39 conjugacy classes of subgroups.

μ_t(G) = 1936

Polycyclic presentation:

2^4,11^2|a^2=d,b^2=c,e^11=f,b^a=bd,e^a=e^10f^10,f^a=f^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1936, 11);