Dic₃×C₁₁⋊C₅×C₁₉⋊C₃ #49178441

order	37620
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₁₁⋊C₅×C₁₉⋊C₃
unambiguous semidirect product	C₃⋊(C₄×C₁₁⋊C₅×C₁₉⋊C₃)
unambiguous semidirect product	(C₁₁×Dic₃)⋊(C₅×C₁₉⋊C₃)
unambiguous semidirect product	(Dic₃×C₁₉)⋊(C₃×C₁₁⋊C₅)
unambiguous semidirect product	(C₁₁×Dic₃×C₁₉⋊C₃)⋊C₅
unambiguous semidirect product	(Dic₃×C₁₉×C₁₁⋊C₅)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×C₁₁⋊C₅×C₁₉⋊C₃
commutator, hypocenter	C₃×C₁₁×C₁₉	C₃×C₄×C₅
Fitting, socle, cosocle	C₂×C₃×C₁₁×C₁₉	C₂×C₃×C₅
prime radical	C₂×C₃×C₁₁⋊C₅×C₁₉⋊C₃	C₂
LCS	G ▷ C₃×C₁₁×C₁₉
UCS	C₁ ◁ C₂

112 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

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

μ_t(G) = 2508

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 150);