Finite Group Databasebeta

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C₇×C₁₉×D₂₁ #19150342

order	5586
isoclinism	isoclinic class of D₂₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₉×D₂₁
unambiguous semidirect product	C₃⋊(C₇×D₇×C₁₉)
unambiguous semidirect product	C₇⋊(D₃×C₇×C₁₉)

Splittings

Fitting, socle, Hall	C₃×C₇²×C₁₉ ⋊ C₂
derived	C₃×C₇ ⋊ C₂×C₇×C₁₉
Hall	C₇²×C₁₉ ⋊ D₃
Hall	C₃×C₇² ⋊ C₂×C₁₉
Hall	C₃×C₁₉ ⋊ C₇×D₇
Sylow	C₇² ⋊ D₃×C₁₉
Sylow	C₃ ⋊ C₇×D₇×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₁₉	D₂₁
commutator, hypocenter	C₃×C₇	C₂×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₇×C₁₉

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1596 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₁₉×D₂₁, D₃×C₇×D₇×C₁₉, C₇×D₂₁⋊D₁₉, …
maximal normal subgroup of	C₇×D₁₉×D₂₁, D₃×C₇×D₇×C₁₉, C₇×D₂₁⋊D₁₉, …
maximal quotient of	C₇×C₁₉×Dic₂₁, C₂×C₇×C₁₉×D₂₁, C₇×C₁₉×D₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5586, 97);