Finite Group Databasebeta

← Prev (#30685387) Next (#30685389) →

D₉×C₂₅×D₁₉ #30685388

order	17100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₉×C₂₅×D₁₉
unambiguous semidirect product	(D₉×C₁₉)⋊(C₂×C₂₅)
unambiguous semidirect product	(C₉×D₁₉)⋊(C₂×C₂₅)
unambiguous semidirect product	D₁₇₁⋊(C₂×C₂₅)

Splittings

Fitting, Hall	C₉×C₁₉×C₂₅ ⋊ C₂²
derived, Hall	C₉×C₁₉ ⋊ C₂²×C₂₅
Hall	C₁₉×C₂₅ ⋊ C₂×D₉
Hall	C₉×C₂₅ ⋊ C₂×D₁₉
Sylow	C₁₉ ⋊ C₂×D₉×C₂₅
Sylow	C₉ ⋊ C₂×C₂₅×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅	D₉×D₁₉
commutator, hypocenter	C₉×C₁₉	C₂²×C₂₅
Frattini	C₃×C₅	C₅×D₃×D₁₉
Fitting	C₉×C₁₉×C₂₅	C₂²
socle	C₃×C₅×C₁₉	C₂×C₅×D₃
prime radical	C₅×D₉×D₁₉	C₅
cosocle	C₅×C₉×C₁₉	C₂²×C₅
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₂₅

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4275

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 25);