C₃×C₁₇×C₁₉×C₁₃⋊C₃ #49180255

order	37791
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₇×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

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

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

48 conjugacy classes of subgroups.

μ_t(G) = 12597

6783 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37791, 12);