C₃×C₅×C₁₉×C₃₇⋊C₃ #44539489

order	31635
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

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

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

48 conjugacy classes of subgroups.

μ_t(G) = 10545

4275 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31635, 20);