C₃×C₅×C₇×A₄×C₁₉ #37561620

order	23940
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅×C₇×C₁₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×C₅×C₇×A₄×C₁₉
unambiguous semidirect product	C₂²⋊(C₃²×C₅×C₇×C₁₉)
unambiguous semidirect product	(C₂²×C₃)⋊(C₃×C₅×C₇×C₁₉)
unambiguous semidirect product	(C₂²×C₅)⋊(C₃²×C₇×C₁₉)
unambiguous semidirect product	(C₂²×C₃×C₅)⋊(C₃×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₃×C₅×C₇×C₁₉	A₄
commutator, cosocle, hypocenter	C₂²	C₃²×C₅×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅×C₇×C₁₉	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₅×C₇×C₁₉

112 conjugacy classes of subgroups.

μ_t(G) = 7980

7980 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 752);