Finite Group Databasebeta

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C₃×C₄×C₁₉×C₅²⋊C₃ #30685676

order	17100
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₁₉ · Schur multiplier (H₂) = C₃×C₅

Aliases

direct product	C₃×C₄×C₁₉×C₅²⋊C₃
unambiguous semidirect product	(C₄×C₅²)⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₃×C₄×C₅²)⋊(C₃×C₁₉)

Splittings

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

Subgroups

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

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3420

Conjugacy classes & character table

2508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 313);