C₅²×D₃×C₁₃×C₁₉ #49150327

order	37050
automorphism	?
homology	Abelianization (H₁) = C₂×C₅²×C₁₃×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×D₃×C₁₃×C₁₉
unambiguous semidirect product	C₃⋊(C₂×C₅²×C₁₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₅²×C₁₃×C₁₉	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅²×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃×C₁₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅²×C₁₃×C₁₉

128 conjugacy classes of subgroups.

μ_t(G) = 18525

18525 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 153);