C₂×C₃×C₁₉×C₄₉⋊C₃ #30660544

order	16758
isoclinism	isoclinic class of C₄₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₂×C₃×C₁₉×C₄₉⋊C₃
unambiguous semidirect product	(C₂×C₄₉)⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₂×C₃×C₄₉)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	C₄₉⋊C₃
commutator, cosocle, hypocenter	C₄₉	C₂×C₃²×C₁₉
Frattini	C₇	C₂×C₃×C₁₉×ΓL(1,𝔽₈)
Fitting	C₂×C₃×C₁₉×C₄₉	C₃
socle	C₂×C₃×C₇×C₁₉	ΓL(1,𝔽₈)
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₂×C₃×C₁₉

72 conjugacy classes of subgroups.

μ_t(G) = 5586

2166 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 71);