D₉×C₁₉×D₅₅ #49178404

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

Aliases

direct product	D₉×C₁₉×D₅₅
unambiguous semidirect product	(C₅×D₉)⋊(C₁₉×D₁₁)
unambiguous semidirect product	(C₁₁×D₉)⋊(D₅×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₉×D₅₅
commutator, cosocle, hypocenter	C₅×C₉×C₁₁	C₂²×C₁₉
Frattini	C₃	D₃×C₁₉×D₅₅
Fitting	C₅×C₉×C₁₁×C₁₉	C₂²
socle	C₃×C₅×C₁₁×C₁₉	C₂×D₃
LCS	G ▷ C₅×C₉×C₁₁
UCS	C₁ ◁ C₁₉

120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.

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

μ_t(G) = 9405

3306 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 113);