C₁₃×C₁₉×(C₅⋊D₅)⋊C₃ #49150243

order	37050
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₃×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₁₃×C₁₉×(C₅⋊D₅)⋊C₃
unambiguous semidirect product	(C₅⋊D₅)⋊(C₃×C₁₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₃×C₁₉	(C₅⋊D₅)⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂×C₃×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₃×C₁₉

48 conjugacy classes of subgroups.

μ_t(G) = 3705

2470 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 69);