C₃×C₅×C₃₇×C₁₉⋊C₃ #44539490

order	31635
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅×C₃₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₅×C₃₇×C₁₉⋊C₃
unambiguous semidirect product	C₁₉⋊(C₃²×C₅×C₃₇)
unambiguous semidirect product	(C₃×C₁₉)⋊(C₃×C₅×C₃₇)
unambiguous semidirect product	(C₅×C₁₉)⋊(C₃²×C₃₇)
unambiguous semidirect product	(C₃×C₅×C₁₉)⋊(C₃×C₃₇)

	subgroup	G/H
center, hypercenter	C₃×C₅×C₃₇	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃²×C₅×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉×C₃₇	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₅×C₃₇

48 conjugacy classes of subgroups.

μ_t(G) = 10545

4995 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31635, 21);