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C₂×C₅×C₁₉×#4294 #44570483

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

Aliases

C₂×C₅×C₁₉×#4294

Splittings

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

Subgroups

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

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1710

Conjugacy classes & character table

5130 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 67);