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C₅×C₁₉×Dic₄₅ #30685452

order	17100
isoclinism	isoclinic class of D₄₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₉×Dic₄₅
unambiguous semidirect product	C₉⋊(C₅×C₁₉×Dic₅)

Splittings

derived	C₅×C₉ ⋊ C₄×C₅×C₁₉
Hall	C₅²×C₉×C₁₉ ⋊ C₄
Hall	C₅²×C₁₉ ⋊ Dic₉
Hall	C₅²×C₉ ⋊ C₄×C₁₉
Hall	C₉×C₁₉ ⋊ C₅×Dic₅
Sylow	C₅² ⋊ C₁₉×Dic₉
Sylow	C₉ ⋊ C₅×C₁₉×Dic₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	D₄₅
commutator, hypocenter	C₅×C₉	C₄×C₅×C₁₉
Frattini	C₂×C₃	C₅×C₁₉×D₁₅
Fitting	C₂×C₅²×C₉×C₁₉	C₂
socle, prime radical	C₂×C₃×C₅²×C₁₉	D₃
cosocle	C₂×C₅×C₉	C₂×C₅×C₁₉
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₅×C₁₉

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3420

Conjugacy classes & character table

4560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 89);