C₃⋊D₃×C₁₉×AGL(1,𝔽₁₁) #49178557

order	37620
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃⋊D₃×C₁₉×AGL(1,𝔽₁₁)
unambiguous semidirect product	D₁₁⋊(C₅×C₃⋊D₃×C₁₉)
unambiguous semidirect product	(C₃×AGL(1,𝔽₁₁))⋊(D₃×C₁₉)
unambiguous semidirect product	(C₃⋊D₃×D₁₁)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₃⋊D₃×C₁₉×D₁₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊D₃×AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₁₉	C₂²×C₅
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₁₉

240 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 1881

1254 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 266);