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C₁₉×D₂₀₇ #21463451

order	7866
isoclinism	isoclinic class of D₂₀₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₂₀₇
unambiguous semidirect product	C₉⋊(C₁₉×D₂₃)
unambiguous semidirect product	C₂₃⋊(D₉×C₁₉)

Splittings

Fitting, Hall	C₉×C₁₉×C₂₃ ⋊ C₂
derived, Hall	C₉×C₂₃ ⋊ C₂×C₁₉
Hall	C₁₉×C₂₃ ⋊ D₉
Hall	C₉×C₁₉ ⋊ D₂₃
Sylow	C₂₃ ⋊ D₉×C₁₉
Sylow	C₉ ⋊ C₁₉×D₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₂₀₇
commutator, hypocenter	C₉×C₂₃	C₂×C₁₉
Frattini	C₃	C₁₉×D₆₉
Fitting	C₉×C₁₉×C₂₃	C₂
socle	C₃×C₁₉×C₂₃	D₃
LCS	G ▷ C₉×C₂₃
UCS	C₁ ◁ C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1995 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×C₁₉×D₂₃, D₁₉×D₂₀₇, D₁₇₁⋊D₂₃, …
maximal normal subgroup of	D₉×C₁₉×D₂₃, D₁₉×D₂₀₇, D₁₇₁⋊D₂₃, …
maximal quotient of	C₁₉×Dic₂₀₇, C₂×C₁₉×D₂₀₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7866, 7);