C₂×C₇×C₁₉×D₄₅ #37561045

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

Aliases

direct product	C₂×C₇×C₁₉×D₄₅
unambiguous semidirect product	(C₂×C₅)⋊(C₇×D₉×C₁₉)
unambiguous semidirect product	(C₂×C₉)⋊(C₇×D₅×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₉	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂²×C₇×C₁₉
Frattini	C₃	C₂×C₇×C₁₉×D₁₅
Fitting	C₂×C₅×C₇×C₉×C₁₉	C₂
socle	C₂×C₃×C₅×C₇×C₁₉	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₇×C₁₉

120 conjugacy classes of subgroups.

μ_t(G) = 11970

6384 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 177);