C₅×D₉×C₁₉×D₁₁ #49178382

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

Aliases

C₅×D₉×C₁₉×D₁₁

	subgroup	G/H
center, hypercenter	C₅×C₁₉	D₉×D₁₁
commutator, cosocle, hypocenter	C₉×C₁₁	C₂²×C₅×C₁₉
Frattini	C₃	C₅×D₃×C₁₉×D₁₁
Fitting	C₅×C₉×C₁₁×C₁₉	C₂²
socle	C₃×C₅×C₁₁×C₁₉	C₂×D₃
LCS	G ▷ C₉×C₁₁
UCS	C₁ ◁ C₅×C₁₉

120 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

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

μ_t(G) = 9405

3990 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 91);