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D₅×C₁₉×#4294 #44570471

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

Aliases

direct product	D₅×C₁₉×#4294
unambiguous semidirect product	C₅⋊(C₂×C₁₉×#4294)

Splittings

derived	C₅×C₁₉ ⋊ C₂×C₉×C₁₉
Hall	C₅×C₁₉×#4294 ⋊ C₂
Hall	D₅×C₁₉² ⋊ C₉
Hall	C₅×C₁₉² ⋊ C₂×C₉
Sylow	C₁₉² ⋊ C₉×D₅
Sylow	C₅ ⋊ C₂×C₁₉×#4294

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₅×C₁₉⋊C₃
commutator, hypocenter	C₅×C₁₉	C₂×C₉×C₁₉
Frattini	C₃	D₅×C₁₉×C₁₉⋊C₃
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
prime radical	C₃×D₅×C₁₉²	C₃
cosocle	C₃×C₅×C₁₉	C₂×C₃×C₁₉
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₃×C₁₉

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 855

Conjugacy classes & character table

2052 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 55);