Finite Group Databasebeta

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C₉×C₃₁×D₁₇ #23748664

order	9486
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₃₁×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂×C₉×C₃₁)

Splittings

Fitting, Hall	C₉×C₁₇×C₃₁ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₉×C₃₁
Hall	C₁₇×C₃₁ ⋊ C₂×C₉
Hall	C₉×C₁₇ ⋊ C₂×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₃₁	D₁₇
commutator, hypocenter	C₁₇	C₂×C₉×C₃₁
Frattini	C₃	C₃×C₃₁×D₁₇
Fitting	C₉×C₁₇×C₃₁	C₂
socle	C₃×C₁₇×C₃₁	C₂×C₃
prime radical	C₃×C₃₁×D₁₇	C₃
cosocle	C₃×C₁₇	C₂×C₃×C₃₁
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₉×C₃₁

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2790 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₃₁×#595, C₉×C₃₁⋊#595, C₉×D₁₇×D₃₁, …
maximal normal subgroup of	C₉×C₃₁×#595, C₉×C₃₁⋊#595, C₉×D₁₇×D₃₁, …
maximal quotient of	C₉×C₃₁×Dic₁₇, C₂×C₉×C₃₁×D₁₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9486, 4);