C₅×C₁₉×C₂²⋊(C₁₃⋊C₃) #28414929

order	14820
isoclinism	isoclinic class of C₂²⋊(C₁₃⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₃×C₅×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×C₁₉×C₂²⋊(C₁₃⋊C₃)
unambiguous semidirect product	C₂²⋊(C₅×C₁₉×C₁₃⋊C₃)
unambiguous semidirect product	C₁₃⋊(C₅×A₄×C₁₉)
unambiguous semidirect product	(C₂²×C₅)⋊(C₁₉×C₁₃⋊C₃)
unambiguous semidirect product	(C₅×C₁₃)⋊(A₄×C₁₉)

	subgroup	G/H
center, hypercenter	C₅×C₁₉	C₂²⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₃	C₃×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₃×C₁₉	C₃
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₅×C₁₉

40 conjugacy classes of subgroups.

μ_t(G) = 4940

1900 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 215);