Finite Group Databasebeta

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C₄×C₁₉×C₅²⋊C₉ #30685443

order	17100
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₄×C₁₉×C₅²⋊C₉
unambiguous semidirect product	(C₄×C₅²)⋊(C₉×C₁₉)

Splittings

derived, Sylow	C₅² ⋊ C₄×C₉×C₁₉
Hall	C₄×C₅²×C₁₉ ⋊ C₉
Hall	C₅²×C₁₉ ⋊ C₄×C₉
Hall	C₄×C₅² ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄×C₁₉	C₅²⋊C₃
commutator, hypocenter	C₅²	C₄×C₉×C₁₉
Frattini	C₂×C₃	C₂×C₁₉×C₅²⋊C₃
Fitting	C₃×C₄×C₅²×C₁₉	C₃
socle, prime radical	C₂×C₃×C₅²×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₅²	C₂×C₃×C₁₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₄×C₁₉

60 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, 80);