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C₉×D₅₂₇ #23748665

order	9486
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₅₂₇
unambiguous semidirect product	C₁₇⋊(C₉×D₃₁)

Splittings

Fitting, Hall	C₉×C₁₇×C₃₁ ⋊ C₂
derived, Hall	C₁₇×C₃₁ ⋊ C₂×C₉
Hall	C₉×C₃₁ ⋊ D₁₇
Hall	C₉×C₁₇ ⋊ D₃₁
Sylow	C₃₁ ⋊ C₉×D₁₇
Sylow	C₁₇ ⋊ C₉×D₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₅₂₇
commutator, hypocenter	C₁₇×C₃₁	C₂×C₉
Frattini	C₃	C₃×D₅₂₇
Fitting	C₉×C₁₇×C₃₁	C₂
socle, cosocle	C₃×C₁₇×C₃₁	C₂×C₃
prime radical	C₃×D₅₂₇	C₃
LCS	G ▷ C₁₇×C₃₁
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2385 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₇×D₃₁, D₉×D₅₂₇, D₁₅₃⋊D₃₁, …
maximal normal subgroup of	C₉×D₁₇×D₃₁, D₉×D₅₂₇, D₁₅₃⋊D₃₁, …
maximal quotient of	C₉×Dic₅₂₇, C₂×C₉×D₅₂₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9486, 5);