C₂×C₁₉×C₉⋊AGL(1,𝔽₁₁) #49178357

order	37620
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₉×C₉⋊AGL(1,𝔽₁₁)
unambiguous semidirect product	(C₂×C₉)⋊(C₁₉×AGL(1,𝔽₁₁))
unambiguous semidirect product	(C₂×C₁₁⋊C₅)⋊(D₉×C₁₉)
unambiguous semidirect product	(C₂×D₉₉)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₂×C₁₉×D₉₉)⋊C₅

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₉⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₉×C₁₁	C₂²×C₅×C₁₉
Frattini	C₃	C₂×C₁₉×C₃⋊AGL(1,𝔽₁₁)
Fitting	C₂×C₉×C₁₁×C₁₉	C₂×C₅
socle	C₂×C₃×C₁₁×C₁₉	C₅×D₃
LCS	G ▷ C₉×C₁₁
UCS	C₁ ◁ C₂×C₁₉

120 conjugacy classes of subgroups.

μ_t(G) = 3762

1482 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 66);