C₃×C₂₃×C₂²⋊(C₁₉⋊C₃) #30628646

order	15732
isoclinism	isoclinic class of C₂²⋊(C₁₉⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₂₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×C₂₃×C₂²⋊(C₁₉⋊C₃)
unambiguous semidirect product	(C₂²×C₃)⋊(C₂₃×C₁₉⋊C₃)
unambiguous semidirect product	(C₃×C₁₉)⋊(A₄×C₂₃)
unambiguous semidirect product	(C₂²×C₃×C₂₃)⋊(C₁₉⋊C₃)
unambiguous semidirect product	(C₃×C₁₉×C₂₃)⋊A₄

	subgroup	G/H
center, hypercenter	C₃×C₂₃	C₂²⋊(C₁₉⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₉	C₃²×C₂₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₉×C₂₃	C₃
LCS	G ▷ C₂²×C₁₉
UCS	C₁ ◁ C₃×C₂₃

56 conjugacy classes of subgroups.

μ_t(G) = 5244

1932 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 108);