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C₅×C₉×C₁₉×D₁₉ #44570495

order	32490
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₅×C₉×C₁₉×D₁₉

Splittings

Fitting, Hall	C₅×C₉×C₁₉² ⋊ C₂
derived	C₁₉ ⋊ C₂×C₅×C₉×C₁₉
Hall	C₉×C₁₉² ⋊ C₂×C₅
Hall	C₅×C₁₉² ⋊ C₂×C₉
Sylow	C₁₉² ⋊ C₂×C₅×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉×C₁₉	D₁₉
commutator, hypocenter	C₁₉	C₂×C₅×C₉×C₁₉
Frattini	C₃	C₃×C₅×C₁₉×D₁₉
Fitting	C₅×C₉×C₁₉²	C₂
socle	C₃×C₅×C₁₉²	C₂×C₃
prime radical	C₃×C₅×C₁₉×D₁₉	C₃
cosocle	C₃×C₁₉	C₂×C₃×C₅×C₁₉
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₅×C₉×C₁₉

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1710

Conjugacy classes & character table

9405 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 79);