C₄₀₁₉⋊C₈ #44565383

order	32152
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₁

Aliases

C₄₀₁₉⋊C₈

C₄₀₁₉ ⋊ C₈

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₄₀₁₉
commutator, hypocenter	C₄₀₁₉	C₈
Fitting, cosocle	C₄×C₄₀₁₉	C₂
socle, prime radical	C₂×C₄₀₁₉	C₄
LCS	G ▷ C₄₀₁₉
UCS	C₁ ◁ C₄

8 conjugacy classes of subgroups.

μ_t(G) = 32152

Polycyclic presentation:

2^3,4019|a^2=b,b^2=c,d^a=d^4018

8044 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32152, 6);