Finite Group Databasebeta

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D₃×C₉×C₁₇ #11745033

order	918
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₉×C₁₇
unambiguous semidirect product	C₃⋊(C₂×C₉×C₁₇)

Splittings

Fitting, Hall	C₃×C₉×C₁₇ ⋊ C₂
derived	C₃ ⋊ C₂×C₉×C₁₇
Sylow	C₃×C₉ ⋊ C₂×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₇	D₃
commutator, hypocenter	C₃	C₂×C₉×C₁₇
Frattini	C₃	C₃×D₃×C₁₇
Fitting	C₃×C₉×C₁₇	C₂
socle	C₃²×C₁₇	C₂×C₃
prime radical	C₃×D₃×C₁₇	C₃
cosocle	C₃²	C₂×C₃×C₁₇
LCS	G ▷ C₃
UCS	C₁ ◁ C₉×C₁₇

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 306

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×C₉×D₁₇, D₃×C₁₇×D₉, D₃×D₁₅₃, …
maximal normal subgroup of	D₃×C₉×D₁₇, D₃×C₁₇×D₉, D₃×D₁₅₃, …
maximal quotient of	C₉×Dic₃×C₁₇, C₂×D₃×C₉×C₁₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(918, 9);