C₅×C₁₉×D₁₅₉ #44475009

order	30210
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₉×D₁₅₉
unambiguous semidirect product	C₃⋊(C₅×C₁₉×D₅₃)
unambiguous semidirect product	C₅₃⋊(C₅×D₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₅×C₁₉	D₁₅₉
commutator, cosocle, hypocenter	C₃×C₅₃	C₂×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉×C₅₃	C₂
LCS	G ▷ C₃×C₅₃
UCS	C₁ ◁ C₅×C₁₉

32 conjugacy classes of subgroups.

μ_t(G) = 15105

7695 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30210, 11);