C₅×C₁₉×C₆₁⋊C₅ #44394284

order	28975
automorphism	?
homology	Abelianization (H₁) = C₅²×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅×C₁₉×C₆₁⋊C₅
unambiguous semidirect product	C₆₁⋊(C₅²×C₁₉)
unambiguous semidirect product	(C₅×C₆₁)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₁₉×C₆₁)⋊C₅²
unambiguous semidirect product	(C₅×C₁₉×C₆₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₅×C₁₉	C₆₁⋊C₅
commutator, cosocle, hypocenter	C₆₁	C₅²×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₆₁	C₅
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₅×C₁₉

32 conjugacy classes of subgroups.

μ_t(G) = 5795

1615 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28975, 4);