Finite Group Databasebeta

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C₂×C₃⋊D₃×C₁₉×C₂₅ #30685525

order	17100
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉×C₂₅ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃⋊D₃×C₁₉×C₂₅
unambiguous semidirect product	(C₂×C₃)⋊(D₃×C₁₉×C₂₅)

Splittings

Fitting	C₂×C₃²×C₁₉×C₂₅ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂²×C₁₉×C₂₅
Hall	C₃²×C₁₉×C₂₅ ⋊ C₂²
Hall	C₃²×C₂₅ ⋊ C₂²×C₁₉
Hall	C₃²×C₁₉ ⋊ C₂²×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₂₅	C₃⋊D₃
commutator, hypocenter	C₃²	C₂²×C₁₉×C₂₅
Frattini	C₅	C₂×C₅×C₃⋊D₃×C₁₉
Fitting	C₂×C₃²×C₁₉×C₂₅	C₂
socle	C₂×C₃²×C₅×C₁₉	C₂×C₅
prime radical	C₂×C₅×C₃⋊D₃×C₁₉	C₅
cosocle	C₃²×C₅	C₂²×C₅×C₁₉
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₉×C₂₅

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8550

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, 162);