C₁₉×D₁₃⋊(C₅²⋊C₃) #49150226

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

Aliases

direct product	C₁₉×D₁₃⋊(C₅²⋊C₃)
unambiguous semidirect product	D₁₃⋊(C₁₉×C₅²⋊C₃)

	subgroup	G/H
center, hypercenter	C₁₉	D₁₃⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₅²×C₁₃	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₁₃
UCS	C₁ ◁ C₁₉

48 conjugacy classes of subgroups.

μ_t(G) = 3705

1368 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 52);