C₁₉×D₅₂₁ #34090187

order	19798
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₅₂₁
unambiguous semidirect product	C₅₂₁⋊(C₂×C₁₉)

Fitting, socle, Hall	C₁₉×C₅₂₁ ⋊ C₂
derived, Sylow	C₅₂₁ ⋊ C₂×C₁₉

	subgroup	G/H
center, hypercenter	C₁₉	D₅₂₁
commutator, cosocle, hypocenter	C₅₂₁	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₅₂₁	C₂
LCS	G ▷ C₅₂₁
UCS	C₁ ◁ C₁₉

8 conjugacy classes of subgroups.

μ_t(G) = 9899

4978 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19798, 2);