C₂×C₃×C₁₉×D₁₂₁ #42119937

order	27588
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×C₁₉×D₁₂₁
unambiguous semidirect product	C₁₂₁⋊(C₂²×C₃×C₁₉)
unambiguous semidirect product	(C₂×C₁₂₁)⋊(C₂×C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₁₂₁
commutator, cosocle, hypocenter	C₁₂₁	C₂²×C₃×C₁₉
Frattini	C₁₁	C₂×C₃×C₁₉×D₁₁
Fitting	C₂×C₃×C₁₉×C₁₂₁	C₂
socle	C₂×C₃×C₁₁×C₁₉	D₁₁
LCS	G ▷ C₁₂₁
UCS	C₁ ◁ C₂×C₃×C₁₉

60 conjugacy classes of subgroups.

μ_t(G) = 13794

7068 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 29);