C₅×C₁₃×C₂²⋊(C₁₉⋊C₃) #28414930

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

Aliases

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

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

40 conjugacy classes of subgroups.

μ_t(G) = 4940

1820 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 216);