Finite Group Databasebeta

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C₂×C₉×C₁₉×D₂₅ #30685398

order	17100
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×C₁₉×D₂₅
unambiguous semidirect product	C₂₅⋊(C₂²×C₉×C₁₉)
unambiguous semidirect product	(C₂×C₂₅)⋊(C₂×C₉×C₁₉)

Splittings

Fitting	C₂×C₉×C₁₉×C₂₅ ⋊ C₂
derived, Sylow	C₂₅ ⋊ C₂²×C₉×C₁₉
Hall	C₉×C₁₉×C₂₅ ⋊ C₂²
Hall	C₁₉×C₂₅ ⋊ C₂²×C₉
Hall	C₉×C₂₅ ⋊ C₂²×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	D₂₅
commutator, hypocenter	C₂₅	C₂²×C₉×C₁₉
Frattini	C₃×C₅	C₂×C₃×D₅×C₁₉
Fitting	C₂×C₉×C₁₉×C₂₅	C₂
socle	C₂×C₃×C₅×C₁₉	C₃×D₅
prime radical	C₂×C₃×C₁₉×D₂₅	C₃
cosocle	C₃×C₂₅	C₂²×C₃×C₁₉
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₉×C₁₉

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8550

Conjugacy classes & character table

4788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 35);