C₄₁₉⋊C₆₄ #41000080

order	26816
automorphism	?
homology	Abelianization (H₁) = C₆₄ · Schur multiplier (H₂) = C₁

Aliases

C₄₁₉⋊C₆₄

C₄₁₉ ⋊ C₆₄

	subgroup	G/H
center, Frattini, hypercenter	C₃₂	D₄₁₉
commutator, hypocenter	C₄₁₉	C₆₄
Fitting, cosocle	C₃₂×C₄₁₉	C₂
socle, prime radical	C₂×C₄₁₉	C₃₂
LCS	G ▷ C₄₁₉
UCS	C₁ ◁ C₃₂

14 conjugacy classes of subgroups.

μ_t(G) = 26816

Polycyclic presentation:

2^6,419|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^418

6752 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26816, 268);