C₃×D₃×C₁₉×D₅₅ #49178692

order	37620
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×D₃×C₁₉×D₅₅
unambiguous semidirect product	(C₅×D₃)⋊(C₃×C₁₉×D₁₁)
unambiguous semidirect product	(D₃×C₁₁)⋊(C₃×D₅×C₁₉)

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₃×D₅₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₁	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁×C₁₉	C₂²
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₃×C₁₉

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

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

μ_t(G) = 6270

4959 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 401);