C₅×C₁₉×C₄₁⋊C₅ #34085771

order	19475
automorphism	?
homology	Abelianization (H₁) = C₅²×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅×C₁₉×C₄₁⋊C₅
unambiguous semidirect product	C₄₁⋊(C₅²×C₁₉)
unambiguous semidirect product	(C₅×C₄₁)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₁₉×C₄₁)⋊C₅²
unambiguous semidirect product	(C₅×C₁₉×C₄₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₅×C₁₉	C₄₁⋊C₅
commutator, cosocle, hypocenter	C₄₁	C₅²×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₄₁	C₅
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₅×C₁₉

32 conjugacy classes of subgroups.

μ_t(G) = 3895

1235 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19475, 4);