C₂×C₁₉×D₂₆₉ #35205505

order	20444
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₉×D₂₆₉
unambiguous semidirect product	C₂₆₉⋊(C₂²×C₁₉)
unambiguous semidirect product	(C₂×C₂₆₉)⋊(C₂×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₂₆₉
commutator, cosocle, hypocenter	C₂₆₉	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₂₆₉	C₂
LCS	G ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₁₉

20 conjugacy classes of subgroups.

μ_t(G) = 10222

5168 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20444, 9);