C₃×C₁₉×D₁₅⋊D₁₁ #49178696

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

Aliases

direct product	C₃×C₁₉×D₁₅⋊D₁₁
unambiguous semidirect product	D₁₅⋊(C₃×C₁₉×D₁₁)
unambiguous semidirect product	D₃₃⋊(C₃×D₅×C₁₉)
unambiguous semidirect product	D₅₅⋊(C₃×D₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₁₅⋊D₁₁
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 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

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

μ_t(G) = 6270

3249 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 405);