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C₂×C₉×C₂₅×D₁₉ #30685397

order	17100
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₂₅ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×C₂₅×D₁₉

Splittings

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

Subgroups

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

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8550

Conjugacy classes & character table

4950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 34);