C₃×C₁₃×C₁₇×C₁₉⋊C₃ #49180254

order	37791
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₃×C₁₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₁₃×C₁₇×C₁₉⋊C₃
unambiguous semidirect product	C₁₉⋊(C₃²×C₁₃×C₁₇)
unambiguous semidirect product	(C₃×C₁₉)⋊(C₃×C₁₃×C₁₇)
unambiguous semidirect product	(C₁₇×C₁₉)⋊(C₃²×C₁₃)
unambiguous semidirect product	(C₃×C₁₇×C₁₉)⋊(C₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₁₇	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃²×C₁₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₇×C₁₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₁₃×C₁₇

48 conjugacy classes of subgroups.

μ_t(G) = 12597

5967 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37791, 11);