C₂×C₃²×C₇×D₅×C₁₉ #37561632

order	23940
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₇×C₁₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃²×C₇×D₅×C₁₉
unambiguous semidirect product	C₅⋊(C₂²×C₃²×C₇×C₁₉)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₃²×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₇×C₁₉	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃²×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₁₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃²×C₇×C₁₉

240 conjugacy classes of subgroups.

μ_t(G) = 11970

9576 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 764);