D₅×D₁₁×#4294 #49178353

order	37620
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₅×D₁₁×#4294
unambiguous semidirect product	(D₅×C₁₁)⋊(C₂×#4294)
unambiguous semidirect product	(C₅×D₁₁)⋊(C₂×#4294)
unambiguous semidirect product	D₅₅⋊(C₂×#4294)

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₅×D₁₁×C₁₉⋊C₃
commutator, hypocenter	C₅×C₁₁×C₁₉	C₂²×C₉
Fitting, socle, cosocle	C₃×C₅×C₁₁×C₁₉	C₂²×C₃
prime radical	C₃×D₅×C₁₉×D₁₁	C₃
LCS	G ▷ C₅×C₁₁×C₁₉
UCS	C₁ ◁ C₃

120 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

μ_t(G) = 9405

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 62);