Finite Group Databasebeta

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C₁₉×C₂₅×Dic₉ #30685372

order	17100
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₂₅×Dic₉
unambiguous semidirect product	C₉⋊(C₄×C₁₉×C₂₅)

Splittings

derived, Sylow	C₉ ⋊ C₄×C₁₉×C₂₅
Hall	C₉×C₁₉×C₂₅ ⋊ C₄
Hall	C₉×C₂₅ ⋊ C₄×C₁₉
Hall	C₉×C₁₉ ⋊ C₄×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₂₅	D₉
commutator, hypocenter	C₉	C₄×C₁₉×C₂₅
Frattini	C₂×C₃×C₅	C₅×D₃×C₁₉
Fitting	C₂×C₉×C₁₉×C₂₅	C₂
socle, prime radical	C₂×C₃×C₅×C₁₉	C₅×D₃
cosocle	C₂×C₅×C₉	C₂×C₅×C₁₉
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₉×C₂₅

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 17100

Conjugacy classes & character table

5700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 9);