C₃×C₁₉×C₂²⋊(C₄₉⋊C₃) #45691444

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×C₁₉×C₂²⋊(C₄₉⋊C₃)
unambiguous semidirect product	(C₂²×C₃)⋊(C₁₉×C₄₉⋊C₃)
unambiguous semidirect product	(C₃×C₄₉)⋊(A₄×C₁₉)

	subgroup	G/H
center, hypercenter	C₃×C₁₉	C₂²⋊(C₄₉⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₄₉	C₃²×C₁₉
Frattini	C₇	C₃×C₁₉×C₂²⋊ΓL(1,𝔽₈)
Fitting	C₂²×C₃×C₁₉×C₄₉	C₃
socle	C₂²×C₃×C₇×C₁₉	ΓL(1,𝔽₈)
LCS	G ▷ C₂²×C₄₉
UCS	C₁ ◁ C₃×C₁₉

84 conjugacy classes of subgroups.

μ_t(G) = 11172

3876 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 242);