Finite Group Databasebeta

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Dic₃×C₁₉×C₅²⋊C₃ #30685671

order	17100
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

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

Splittings

derived	C₃×C₅² ⋊ C₃×C₄×C₁₉
Hall	C₃×C₁₉×C₅²⋊C₃ ⋊ C₄
Hall	C₅²×C₁₉ ⋊ C₃×Dic₃
Hall	C₃×C₅²⋊C₃ ⋊ C₄×C₁₉
Sylow	C₅² ⋊ C₃×Dic₃×C₁₉

Subgroups

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

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3420

Conjugacy classes & character table

1254 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 308);