C₅×A₄×C₁₉×C₂₃ #39910797

order	26220
automorphism	?
homology	Abelianization (H₁) = C₃×C₅×C₁₉×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×A₄×C₁₉×C₂₃
unambiguous semidirect product	C₂²⋊(C₃×C₅×C₁₉×C₂₃)
unambiguous semidirect product	(C₂²×C₅)⋊(C₃×C₁₉×C₂₃)
unambiguous semidirect product	(C₂²×C₂₃)⋊(C₃×C₅×C₁₉)
unambiguous semidirect product	(C₂²×C₅×C₂₃)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₅×C₁₉×C₂₃	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₅×C₁₉×C₂₃
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₉×C₂₃	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₅×C₁₉×C₂₃

40 conjugacy classes of subgroups.

μ_t(G) = 8740

8740 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 87);