Finite Group Databasebeta

← Prev (#30685652) Next (#30685654) →

C₃×C₁₉×#1039⋊C₃ #30685653

order	17100
isoclinism	isoclinic class of (C₅⋊D₅)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₁₉ · Schur multiplier (H₂) = C₃×C₅

Aliases

direct product	C₃×C₁₉×#1039⋊C₃
unambiguous semidirect product	#1039⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₃×#1039)⋊(C₃×C₁₉)

Splittings

derived, Sylow	C₅² ⋊ C₃²×C₄×C₁₉
Hall	C₃×C₁₉×C₅²⋊C₃ ⋊ C₄
Hall	C₁₉×#1039 ⋊ C₃²
Hall	C₅²×C₁₉ ⋊ C₃²×C₄
Hall	C₃×C₅²⋊C₃ ⋊ C₄×C₁₉
Hall	#1039 ⋊ C₃²×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	(C₅⋊D₅)⋊C₃
commutator, hypocenter	C₅²	C₃²×C₄×C₁₉
Frattini	C₂	C₃×C₁₉×(C₅⋊D₅)⋊C₃
Fitting, 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 ◁ C₂×C₃×C₁₉

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3420

Conjugacy classes & character table

1140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 290);