D₉×D₁₉×C₁₁⋊C₅ #49178339

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

Aliases

direct product	D₉×D₁₉×C₁₁⋊C₅
unambiguous semidirect product	(D₉×C₁₉)⋊(C₂×C₁₁⋊C₅)
unambiguous semidirect product	(C₉×D₁₉)⋊(C₂×C₁₁⋊C₅)
unambiguous semidirect product	D₁₇₁⋊(C₂×C₁₁⋊C₅)
unambiguous semidirect product	(C₁₁×D₉×D₁₉)⋊C₅

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₁×C₁₉	C₂²×C₅
Frattini	C₃	D₃×D₁₉×C₁₁⋊C₅
socle	C₃×C₁₁×C₁₉	C₂×C₅×D₃
LCS	G ▷ C₉×C₁₁×C₁₉
UCS	C₁

120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.

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

μ_t(G) = 1881

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 48);