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C₉×D₄₂₇ #21440243

order	7686
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₄₂₇

Splittings

Fitting, Hall	C₇×C₉×C₆₁ ⋊ C₂
derived, Hall	C₇×C₆₁ ⋊ C₂×C₉
Hall	C₉×C₆₁ ⋊ D₇
Hall	C₇×C₉ ⋊ D₆₁
Sylow	C₆₁ ⋊ C₉×D₇
Sylow	C₇ ⋊ C₉×D₆₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₄₂₇
commutator, hypocenter	C₇×C₆₁	C₂×C₉
Frattini	C₃	C₃×D₄₂₇
Fitting	C₇×C₉×C₆₁	C₂
socle	C₃×C₇×C₆₁	C₂×C₃
LCS	G ▷ C₇×C₆₁
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1935 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₆₁, D₉×D₄₂₇, D₆₃⋊D₆₁, …
maximal normal subgroup of	C₉×D₇×D₆₁, D₉×D₄₂₇, D₆₃⋊D₆₁, …
maximal quotient of	C₉×Dic₄₂₇, C₂×C₉×D₄₂₇, C₅×C₉×D₄₂₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7686, 8);