Finite Group Databasebeta

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C₃×C₅²×Dic₃×C₁₉ #30685683

order	17100
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₅²×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₃×C₅²×Dic₃×C₁₉
unambiguous semidirect product	C₃⋊(C₃×C₄×C₅²×C₁₉)

Splittings

derived	C₃ ⋊ C₃×C₄×C₅²×C₁₉
Hall	C₃²×C₅²×C₁₉ ⋊ C₄
Hall	C₃²×C₅² ⋊ C₄×C₁₉
Hall	C₃²×C₁₉ ⋊ C₄×C₅²
Sylow	C₃² ⋊ C₄×C₅²×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅²×C₁₉	D₃
commutator, hypocenter	C₃	C₃×C₄×C₅²×C₁₉
Frattini	C₂	C₃×C₅²×D₃×C₁₉
Fitting, socle, prime radical	C₂×C₃²×C₅²×C₁₉	C₂
cosocle	C₂×C₃	C₂×C₃×C₅²×C₁₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₅²×C₁₉

224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 5700

Conjugacy classes & character table

8550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 320);